{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Python for Finance (2nd ed.)\n",
    "\n",
    "**Mastering Data-Driven Finance**\n",
    "\n",
    "&copy; Dr. Yves J. Hilpisch | The Python Quants GmbH\n",
    "\n",
    "<img src=\"http://hilpisch.com/images/py4fi_2nd_shadow.png\" width=\"300px\" align=\"left\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Statistics (a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Normality Tests"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Benchmark Case"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "uuid": "b5c2a3e0-81d2-4aab-bee0-a9239fc9ffa6"
   },
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import scipy.stats as scs\n",
    "import statsmodels.api as sm\n",
    "from pylab import mpl, plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.style.use('seaborn')\n",
    "mpl.rcParams['font.family'] = 'serif'\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "uuid": "596ccb67-e163-4f15-95e8-80362bdade98"
   },
   "outputs": [],
   "source": [
    "def gen_paths(S0, r, sigma, T, M, I):\n",
    "    ''' Generate Monte Carlo paths for geometric Brownian motion.\n",
    "    \n",
    "    Parameters\n",
    "    ==========\n",
    "    S0: float\n",
    "        initial stock/index value\n",
    "    r: float\n",
    "        constant short rate\n",
    "    sigma: float\n",
    "        constant volatility\n",
    "    T: float\n",
    "        final time horizon\n",
    "    M: int\n",
    "        number of time steps/intervals\n",
    "    I: int\n",
    "        number of paths to be simulated\n",
    "        \n",
    "    Returns\n",
    "    =======\n",
    "    paths: ndarray, shape (M + 1, I)\n",
    "        simulated paths given the parameters\n",
    "    '''\n",
    "    dt = T / M\n",
    "    paths = np.zeros((M + 1, I))\n",
    "    paths[0] = S0\n",
    "    for t in range(1, M + 1):\n",
    "        rand = np.random.standard_normal(I)\n",
    "        rand = (rand - rand.mean()) / rand.std()  \n",
    "        paths[t] = paths[t - 1] * np.exp((r - 0.5 * sigma ** 2) * dt +\n",
    "                                         sigma * math.sqrt(dt) * rand)  \n",
    "    return paths"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "uuid": "7b6ba027-7f3c-43ee-a297-66599a4c9ac2"
   },
   "outputs": [],
   "source": [
    "S0 = 100.  \n",
    "r = 0.05  \n",
    "sigma = 0.2  \n",
    "T = 1.0   \n",
    "M = 50  \n",
    "I = 250000  \n",
    "np.random.seed(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "uuid": "abdf423c-dc32-4528-8781-12e05a6703cd"
   },
   "outputs": [],
   "source": [
    "paths = gen_paths(S0, r, sigma, T, M, I)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "105.12710963760242"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S0 * math.exp(r * T)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "105.12645392478755"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "paths[-1].mean()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "uuid": "133e6168-692d-4aa7-8b8d-81d21e1d21e9"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(paths[:, :10])\n",
    "plt.xlabel('time steps')\n",
    "plt.ylabel('index level');\n",
    "# plt.savefig('../../images/ch13/stat_01.png');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "uuid": "4fe20e49-2c58-454c-a086-14c2f2901dba"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([100.    ,  97.821 ,  98.5573, 106.1546, 105.899 ,  99.8363,\n",
       "       100.0145, 102.6589, 105.6643, 107.1107, 108.7943, 108.2449,\n",
       "       106.4105, 101.0575, 102.0197, 102.6052, 109.6419, 109.5725,\n",
       "       112.9766, 113.0225, 112.5476, 114.5585, 109.942 , 112.6271,\n",
       "       112.7502, 116.3453, 115.0443, 113.9586, 115.8831, 117.3705,\n",
       "       117.9185, 110.5539, 109.9687, 104.9957, 108.0679, 105.7822,\n",
       "       105.1585, 104.3304, 108.4387, 105.5963, 108.866 , 108.3284,\n",
       "       107.0077, 106.0034, 104.3964, 101.0637,  98.3776,  97.135 ,\n",
       "        95.4254,  96.4271,  96.3386])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "paths[:, 0].round(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "uuid": "c9a7ad7d-921d-4b03-a81e-bff7d6e60b8e"
   },
   "outputs": [],
   "source": [
    "log_returns = np.log(paths[1:] / paths[:-1]) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "uuid": "cd6ee063-9463-405d-96bd-2ad1231d7e7f"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.022 ,  0.0075,  0.0743, -0.0024, -0.059 ,  0.0018,  0.0261,\n",
       "        0.0289,  0.0136,  0.0156, -0.0051, -0.0171, -0.0516,  0.0095,\n",
       "        0.0057,  0.0663, -0.0006,  0.0306,  0.0004, -0.0042,  0.0177,\n",
       "       -0.0411,  0.0241,  0.0011,  0.0314, -0.0112, -0.0095,  0.0167,\n",
       "        0.0128,  0.0047, -0.0645, -0.0053, -0.0463,  0.0288, -0.0214,\n",
       "       -0.0059, -0.0079,  0.0386, -0.0266,  0.0305, -0.0049, -0.0123,\n",
       "       -0.0094, -0.0153, -0.0324, -0.0269, -0.0127, -0.0178,  0.0104,\n",
       "       -0.0009])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_returns[:, 0].round(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings; warnings.simplefilter('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "uuid": "77290ae6-4035-42a6-8312-ec89da50f88b"
   },
   "outputs": [],
   "source": [
    "def print_statistics(array):\n",
    "    ''' Prints selected statistics.\n",
    "    \n",
    "    Parameters\n",
    "    ==========\n",
    "    array: ndarray\n",
    "        object to generate statistics on\n",
    "    '''\n",
    "    sta = scs.describe(array)\n",
    "    print('%14s %15s' % ('statistic', 'value'))\n",
    "    print(30 * '-')\n",
    "    print('%14s %15.5f' % ('size', sta[0]))\n",
    "    print('%14s %15.5f' % ('min', sta[1][0]))\n",
    "    print('%14s %15.5f' % ('max', sta[1][1]))\n",
    "    print('%14s %15.5f' % ('mean', sta[2]))\n",
    "    print('%14s %15.5f' % ('std', np.sqrt(sta[3])))\n",
    "    print('%14s %15.5f' % ('skew', sta[4]))\n",
    "    print('%14s %15.5f' % ('kurtosis', sta[5]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "uuid": "57ac0ad6-14c7-4158-b67b-b553d662dc21"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     statistic           value\n",
      "------------------------------\n",
      "          size  12500000.00000\n",
      "           min        -0.15664\n",
      "           max         0.15371\n",
      "          mean         0.00060\n",
      "           std         0.02828\n",
      "          skew         0.00055\n",
      "      kurtosis         0.00085\n"
     ]
    }
   ],
   "source": [
    "print_statistics(log_returns.flatten())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.05000000000000006"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_returns.mean() * M + 0.5 * sigma ** 2  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.20000000000000015"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_returns.std() * math.sqrt(M)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "uuid": "1bb98c2c-002b-4e19-88af-ae23db1a673f"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.hist(log_returns.flatten(), bins=70, density=True,\n",
    "         label='frequency', color='b')\n",
    "plt.xlabel('log return')\n",
    "plt.ylabel('frequency')\n",
    "x = np.linspace(plt.axis()[0], plt.axis()[1])\n",
    "plt.plot(x, scs.norm.pdf(x, loc=r / M, scale=sigma / np.sqrt(M)),\n",
    "         'r', lw=2.0, label='pdf')  \n",
    "plt.legend();\n",
    "# plt.savefig('../../images/ch13/stat_02.png');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "uuid": "75c069e5-c518-4fca-8b60-de465ba1a56b"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sm.qqplot(log_returns.flatten()[::500], line='s')\n",
    "plt.xlabel('theoretical quantiles')\n",
    "plt.ylabel('sample quantiles');\n",
    "# plt.savefig('../../images/ch13/stat_03.png');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "uuid": "a6e5cdd2-0e90-4b34-8c13-d52dfe7e897b"
   },
   "outputs": [],
   "source": [
    "def normality_tests(arr):\n",
    "    ''' Tests for normality distribution of given data set.\n",
    "    \n",
    "    Parameters\n",
    "    ==========\n",
    "    array: ndarray\n",
    "        object to generate statistics on\n",
    "    '''\n",
    "    print('Skew of data set  %14.3f' % scs.skew(arr))\n",
    "    print('Skew test p-value %14.3f' % scs.skewtest(arr)[1])\n",
    "    print('Kurt of data set  %14.3f' % scs.kurtosis(arr))\n",
    "    print('Kurt test p-value %14.3f' % scs.kurtosistest(arr)[1])\n",
    "    print('Norm test p-value %14.3f' % scs.normaltest(arr)[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "uuid": "d35f18c9-d798-47f7-85d4-dc09b0907134"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Skew of data set           0.001\n",
      "Skew test p-value          0.430\n",
      "Kurt of data set           0.001\n",
      "Kurt test p-value          0.541\n",
      "Norm test p-value          0.607\n"
     ]
    }
   ],
   "source": [
    "normality_tests(log_returns.flatten())  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "uuid": "80629df6-776e-4849-872b-46b6b35d4eb0"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'log data')"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 6))\n",
    "ax1.hist(paths[-1], bins=30)\n",
    "ax1.set_xlabel('index level')\n",
    "ax1.set_ylabel('frequency')\n",
    "ax1.set_title('regular data')\n",
    "ax2.hist(np.log(paths[-1]), bins=30)\n",
    "ax2.set_xlabel('log index level')\n",
    "ax2.set_title('log data')\n",
    "# plt.savefig('../../images/ch13/stat_04.png');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "uuid": "9e7b6096-9d21-4199-882b-b38f760fc72e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     statistic           value\n",
      "------------------------------\n",
      "          size    250000.00000\n",
      "           min        42.74870\n",
      "           max       233.58435\n",
      "          mean       105.12645\n",
      "           std        21.23174\n",
      "          skew         0.61116\n",
      "      kurtosis         0.65182\n"
     ]
    }
   ],
   "source": [
    "print_statistics(paths[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "uuid": "b9b2eab0-7788-48f7-b4b2-c3f1e263f0b6"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     statistic           value\n",
      "------------------------------\n",
      "          size    250000.00000\n",
      "           min         3.75534\n",
      "           max         5.45354\n",
      "          mean         4.63517\n",
      "           std         0.19998\n",
      "          skew        -0.00092\n",
      "      kurtosis        -0.00327\n"
     ]
    }
   ],
   "source": [
    "print_statistics(np.log(paths[-1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "uuid": "7bd3a6dc-ca9f-4878-bf30-27127547b952"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Skew of data set          -0.001\n",
      "Skew test p-value          0.851\n",
      "Kurt of data set          -0.003\n",
      "Kurt test p-value          0.744\n",
      "Norm test p-value          0.931\n"
     ]
    }
   ],
   "source": [
    "normality_tests(np.log(paths[-1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "uuid": "fbe45821-3fda-4924-9b65-b7aae6004ae6"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "log_data = np.log(paths[-1])\n",
    "plt.hist(log_data, bins=70, density=True,\n",
    "         label='observed', color='b')\n",
    "plt.xlabel('index levels')\n",
    "plt.ylabel('frequency')\n",
    "x = np.linspace(plt.axis()[0], plt.axis()[1])\n",
    "plt.plot(x, scs.norm.pdf(x, log_data.mean(), log_data.std()),\n",
    "         'r', lw=2.0, label='pdf')\n",
    "plt.legend();\n",
    "# plt.savefig('../../images/ch13/stat_05.png');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "uuid": "1db3cb57-4537-4e8c-96ca-9a96cb35bf99"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sm.qqplot(log_data, line='s')\n",
    "plt.xlabel('theoretical quantiles')\n",
    "plt.ylabel('sample quantiles');\n",
    "# plt.savefig('../../images/ch13/stat_06.png');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Real World Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "uuid": "2fac84d1-67fd-4345-a9b8-58e8e20b6ea6"
   },
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "raw = pd.read_csv('../../source/tr_eikon_eod_data.csv',\n",
    "                 index_col=0, parse_dates=True).dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "uuid": "8c2cddba-d3fc-4e22-8b22-b0a6dcf61f16"
   },
   "outputs": [],
   "source": [
    "symbols = ['SPY', 'GLD', 'AAPL.O', 'MSFT.O']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "uuid": "eaa5651f-3c91-4f0f-9941-b564e4b7dbe1"
   },
   "outputs": [],
   "source": [
    "data = raw[symbols]\n",
    "data = data.dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "uuid": "e4574de5-c00f-4665-b341-dad771d24d8e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "DatetimeIndex: 2138 entries, 2010-01-04 to 2018-06-29\n",
      "Data columns (total 4 columns):\n",
      " #   Column  Non-Null Count  Dtype  \n",
      "---  ------  --------------  -----  \n",
      " 0   SPY     2138 non-null   float64\n",
      " 1   GLD     2138 non-null   float64\n",
      " 2   AAPL.O  2138 non-null   float64\n",
      " 3   MSFT.O  2138 non-null   float64\n",
      "dtypes: float64(4)\n",
      "memory usage: 83.5 KB\n"
     ]
    }
   ],
   "source": [
    "data.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "uuid": "f2acb16d-fd16-4008-95a7-5213e3df3a9e"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SPY</th>\n",
       "      <th>GLD</th>\n",
       "      <th>AAPL.O</th>\n",
       "      <th>MSFT.O</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2010-01-04</th>\n",
       "      <td>113.33</td>\n",
       "      <td>109.80</td>\n",
       "      <td>30.572827</td>\n",
       "      <td>30.950</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-01-05</th>\n",
       "      <td>113.63</td>\n",
       "      <td>109.70</td>\n",
       "      <td>30.625684</td>\n",
       "      <td>30.960</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-01-06</th>\n",
       "      <td>113.71</td>\n",
       "      <td>111.51</td>\n",
       "      <td>30.138541</td>\n",
       "      <td>30.770</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-01-07</th>\n",
       "      <td>114.19</td>\n",
       "      <td>110.82</td>\n",
       "      <td>30.082827</td>\n",
       "      <td>30.452</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-01-08</th>\n",
       "      <td>114.57</td>\n",
       "      <td>111.37</td>\n",
       "      <td>30.282827</td>\n",
       "      <td>30.660</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               SPY     GLD     AAPL.O  MSFT.O\n",
       "Date                                         \n",
       "2010-01-04  113.33  109.80  30.572827  30.950\n",
       "2010-01-05  113.63  109.70  30.625684  30.960\n",
       "2010-01-06  113.71  111.51  30.138541  30.770\n",
       "2010-01-07  114.19  110.82  30.082827  30.452\n",
       "2010-01-08  114.57  111.37  30.282827  30.660"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "uuid": "d4cf7b80-4be5-48d6-b669-acf6c9784941"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fd8b97cb890>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "(data / data.iloc[0] * 100).plot(figsize=(10, 6))\n",
    "# plt.savefig('../../images/ch13/stat_07.png');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "uuid": "8caf3129-34cb-4ce0-a53b-bef84d3db2dc"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SPY</th>\n",
       "      <th>GLD</th>\n",
       "      <th>AAPL.O</th>\n",
       "      <th>MSFT.O</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2010-01-04</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-01-05</th>\n",
       "      <td>0.002644</td>\n",
       "      <td>-0.000911</td>\n",
       "      <td>0.001727</td>\n",
       "      <td>0.000323</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-01-06</th>\n",
       "      <td>0.000704</td>\n",
       "      <td>0.016365</td>\n",
       "      <td>-0.016034</td>\n",
       "      <td>-0.006156</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-01-07</th>\n",
       "      <td>0.004212</td>\n",
       "      <td>-0.006207</td>\n",
       "      <td>-0.001850</td>\n",
       "      <td>-0.010389</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-01-08</th>\n",
       "      <td>0.003322</td>\n",
       "      <td>0.004951</td>\n",
       "      <td>0.006626</td>\n",
       "      <td>0.006807</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 SPY       GLD    AAPL.O    MSFT.O\n",
       "Date                                              \n",
       "2010-01-04       NaN       NaN       NaN       NaN\n",
       "2010-01-05  0.002644 -0.000911  0.001727  0.000323\n",
       "2010-01-06  0.000704  0.016365 -0.016034 -0.006156\n",
       "2010-01-07  0.004212 -0.006207 -0.001850 -0.010389\n",
       "2010-01-08  0.003322  0.004951  0.006626  0.006807"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_returns = np.log(data / data.shift(1))\n",
    "log_returns.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "uuid": "f6fefbe1-3ec6-4d1b-b774-9db3f3c38c83"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "log_returns.hist(bins=50, figsize=(10, 8));\n",
    "# plt.savefig('../../images/ch13/stat_08.png');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "uuid": "5e6f48e5-68f2-44ec-ad92-635ad3c249ec"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Results for symbol SPY\n",
      "------------------------------\n",
      "     statistic           value\n",
      "------------------------------\n",
      "          size      2137.00000\n",
      "           min        -0.06734\n",
      "           max         0.04545\n",
      "          mean         0.00041\n",
      "           std         0.00933\n",
      "          skew        -0.52189\n",
      "      kurtosis         4.52432\n",
      "\n",
      "Results for symbol GLD\n",
      "------------------------------\n",
      "     statistic           value\n",
      "------------------------------\n",
      "          size      2137.00000\n",
      "           min        -0.09191\n",
      "           max         0.04795\n",
      "          mean         0.00004\n",
      "           std         0.01020\n",
      "          skew        -0.59934\n",
      "      kurtosis         5.68423\n",
      "\n",
      "Results for symbol AAPL.O\n",
      "------------------------------\n",
      "     statistic           value\n",
      "------------------------------\n",
      "          size      2137.00000\n",
      "           min        -0.13187\n",
      "           max         0.08502\n",
      "          mean         0.00084\n",
      "           std         0.01591\n",
      "          skew        -0.23510\n",
      "      kurtosis         4.78964\n",
      "\n",
      "Results for symbol MSFT.O\n",
      "------------------------------\n",
      "     statistic           value\n",
      "------------------------------\n",
      "          size      2137.00000\n",
      "           min        -0.12103\n",
      "           max         0.09941\n",
      "          mean         0.00054\n",
      "           std         0.01421\n",
      "          skew        -0.09117\n",
      "      kurtosis         7.29106\n"
     ]
    }
   ],
   "source": [
    "for sym in symbols:\n",
    "    print('\\nResults for symbol {}'.format(sym))\n",
    "    print(30 * '-')\n",
    "    log_data = np.array(log_returns[sym].dropna())\n",
    "    print_statistics(log_data)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "uuid": "83fc3d8b-03c4-43bc-a7a3-b7ac0747c2b1"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sm.qqplot(log_returns['SPY'].dropna(), line='s')\n",
    "plt.title('SPY')\n",
    "plt.xlabel('theoretical quantiles')\n",
    "plt.ylabel('sample quantiles');\n",
    "# plt.savefig('../../images/ch13/stat_09.png');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "uuid": "a6e1cee5-aebc-4c63-8ce4-100562f31859"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sm.qqplot(log_returns['MSFT.O'].dropna(), line='s')\n",
    "plt.title('MSFT.O')\n",
    "plt.xlabel('theoretical quantiles')\n",
    "plt.ylabel('sample quantiles');\n",
    "# plt.savefig('../../images/ch13/stat_10.png');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "uuid": "bce2aa32-77f9-4d5a-9a81-1a37b6b90001"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Results for symbol SPY\n",
      "--------------------------------\n",
      "Skew of data set          -0.522\n",
      "Skew test p-value          0.000\n",
      "Kurt of data set           4.524\n",
      "Kurt test p-value          0.000\n",
      "Norm test p-value          0.000\n",
      "\n",
      "Results for symbol GLD\n",
      "--------------------------------\n",
      "Skew of data set          -0.599\n",
      "Skew test p-value          0.000\n",
      "Kurt of data set           5.684\n",
      "Kurt test p-value          0.000\n",
      "Norm test p-value          0.000\n",
      "\n",
      "Results for symbol AAPL.O\n",
      "--------------------------------\n",
      "Skew of data set          -0.235\n",
      "Skew test p-value          0.000\n",
      "Kurt of data set           4.790\n",
      "Kurt test p-value          0.000\n",
      "Norm test p-value          0.000\n",
      "\n",
      "Results for symbol MSFT.O\n",
      "--------------------------------\n",
      "Skew of data set          -0.091\n",
      "Skew test p-value          0.085\n",
      "Kurt of data set           7.291\n",
      "Kurt test p-value          0.000\n",
      "Norm test p-value          0.000\n"
     ]
    }
   ],
   "source": [
    "for sym in symbols:\n",
    "    print('\\nResults for symbol {}'.format(sym))\n",
    "    print(32 * '-')\n",
    "    log_data = np.array(log_returns[sym].dropna())\n",
    "    normality_tests(log_data)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Portfolio Optimization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "uuid": "74a583b1-1e85-4efa-adf0-c70377606aa6"
   },
   "outputs": [],
   "source": [
    "symbols = ['AAPL.O', 'MSFT.O', 'SPY', 'GLD']  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "uuid": "74a583b1-1e85-4efa-adf0-c70377606aa6"
   },
   "outputs": [],
   "source": [
    "noa = len(symbols)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "uuid": "23729711-44d9-49a9-9c10-8d238be308cb"
   },
   "outputs": [],
   "source": [
    "data = raw[symbols]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "uuid": "e7e3d4af-6b03-4b05-9bb2-69132aa9b96d"
   },
   "outputs": [],
   "source": [
    "rets = np.log(data / data.shift(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "uuid": "2bd5a671-fb77-4c78-90d9-bef99c34af86"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rets.hist(bins=40, figsize=(10, 8));\n",
    "# plt.savefig('../../images/ch13/stat_11.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "uuid": "3416c8ac-7ee5-4c5d-a929-92aa2881382d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "AAPL.O    0.212359\n",
       "MSFT.O    0.136648\n",
       "SPY       0.102928\n",
       "GLD       0.009141\n",
       "dtype: float64"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rets.mean() * 252  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "uuid": "437bb447-a4b0-4ddc-97de-965d2cb6c9f2"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AAPL.O</th>\n",
       "      <th>MSFT.O</th>\n",
       "      <th>SPY</th>\n",
       "      <th>GLD</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>AAPL.O</th>\n",
       "      <td>0.063773</td>\n",
       "      <td>0.023427</td>\n",
       "      <td>0.021039</td>\n",
       "      <td>0.001513</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MSFT.O</th>\n",
       "      <td>0.023427</td>\n",
       "      <td>0.050917</td>\n",
       "      <td>0.022244</td>\n",
       "      <td>-0.000347</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SPY</th>\n",
       "      <td>0.021039</td>\n",
       "      <td>0.022244</td>\n",
       "      <td>0.021939</td>\n",
       "      <td>0.000062</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GLD</th>\n",
       "      <td>0.001513</td>\n",
       "      <td>-0.000347</td>\n",
       "      <td>0.000062</td>\n",
       "      <td>0.026209</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          AAPL.O    MSFT.O       SPY       GLD\n",
       "AAPL.O  0.063773  0.023427  0.021039  0.001513\n",
       "MSFT.O  0.023427  0.050917  0.022244 -0.000347\n",
       "SPY     0.021039  0.022244  0.021939  0.000062\n",
       "GLD     0.001513 -0.000347  0.000062  0.026209"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rets.cov() * 252  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Basic Theory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "uuid": "3d86ff5b-9de8-4cee-99ea-cc01e4697320"
   },
   "outputs": [],
   "source": [
    "weights = np.random.random(noa)  \n",
    "weights /= np.sum(weights)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "uuid": "9d9499c0-c033-4d4a-b2d4-e8ef064eb9ae"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.07650728, 0.06021919, 0.63364218, 0.22963135])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "scrolled": true,
    "uuid": "9d9499c0-c033-4d4a-b2d4-e8ef064eb9ae"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weights.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "uuid": "c9ec5dc3-df96-4418-90fe-0e76ed7b006d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.09179459482057793"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(rets.mean() * weights) * 252  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "uuid": "40f68bdb-74ea-4f6d-9f93-c498a9a13167"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.014763288666485574"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(weights.T, np.dot(rets.cov() * 252, weights))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "uuid": "351e317e-5f22-474b-b1a5-1f2934f608a1"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.12150427427249452"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.sqrt(np.dot(weights.T, np.dot(rets.cov() * 252, weights)))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "def port_ret(weights):\n",
    "    return np.sum(rets.mean() * weights) * 252"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "def port_vol(weights):\n",
    "    return np.sqrt(np.dot(weights.T, np.dot(rets.cov() * 252, weights)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "uuid": "689bff52-80a9-48ac-9fce-0855e2a763ae"
   },
   "outputs": [],
   "source": [
    "prets = []\n",
    "pvols = []\n",
    "for p in range (2500):  \n",
    "    weights = np.random.random(noa)  \n",
    "    weights /= np.sum(weights)  \n",
    "    prets.append(port_ret(weights))  \n",
    "    pvols.append(port_vol(weights))  \n",
    "prets = np.array(prets)\n",
    "pvols = np.array(pvols)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "uuid": "81d7f822-79e9-41bb-94b1-649807788f2e"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.scatter(pvols, prets, c=prets / pvols,\n",
    "            marker='o', cmap='coolwarm')\n",
    "plt.xlabel('expected volatility')\n",
    "plt.ylabel('expected return')\n",
    "plt.colorbar(label='Sharpe ratio');\n",
    "# plt.savefig('../../images/ch13/stat_12.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Portfolio Optimizations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "uuid": "1fea02c0-d092-4a29-a9eb-2d4022985a62"
   },
   "outputs": [],
   "source": [
    "import scipy.optimize as sco"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "uuid": "0124792d-7b7f-4f7c-ac42-367681a7145f"
   },
   "outputs": [],
   "source": [
    "def min_func_sharpe(weights):  \n",
    "    return -port_ret(weights) / port_vol(weights)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "uuid": "a634bb6a-ef2e-4a68-9414-b2e320b58296"
   },
   "outputs": [],
   "source": [
    "cons = ({'type': 'eq', 'fun': lambda x:  np.sum(x) - 1})  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "uuid": "40e6c1b4-8fb8-4a8f-b2ba-36ffdaefc47b"
   },
   "outputs": [],
   "source": [
    "bnds = tuple((0, 1) for x in range(noa))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "uuid": "d689f1b3-c680-4a1e-865b-85a64b06c0f6"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.25, 0.25, 0.25, 0.25])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eweights = np.array(noa * [1. / noa,])  \n",
    "eweights  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.8436203363155397"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "min_func_sharpe(eweights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "uuid": "dda15397-398b-445e-be6a-11e7ed0e3c32"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 67.2 ms, sys: 3.27 ms, total: 70.5 ms\n",
      "Wall time: 81.6 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "opts = sco.minimize(min_func_sharpe, eweights,\n",
    "                    method='SLSQP', bounds=bnds,\n",
    "                    constraints=cons)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "uuid": "ee237054-2af4-4879-97d1-0ee77d84d9a8"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "     fun: -0.8976673894123512\n",
       "     jac: array([ 8.96975398e-05,  8.30292702e-05, -2.45958567e-04,  1.92746520e-05])\n",
       " message: 'Optimization terminated successfully.'\n",
       "    nfev: 36\n",
       "     nit: 6\n",
       "    njev: 6\n",
       "  status: 0\n",
       " success: True\n",
       "       x: array([0.51191356, 0.19126411, 0.25454111, 0.04228122])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opts  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "uuid": "e0a821b0-a330-4979-bec2-a9e731f11656"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.512, 0.191, 0.255, 0.042])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opts['x'].round(3)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "uuid": "faae2c2f-382b-427b-9426-87085a339b76"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.161"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "port_ret(opts['x']).round(3)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "uuid": "faae2c2f-382b-427b-9426-87085a339b76"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.18"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "port_vol(opts['x']).round(3)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8976673894123512"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "port_ret(opts['x']) / port_vol(opts['x'])  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "uuid": "f84ed951-5f9b-4ec7-bb7c-330994bdb0b9"
   },
   "outputs": [],
   "source": [
    "optv = sco.minimize(port_vol, eweights,\n",
    "                    method='SLSQP', bounds=bnds,\n",
    "                    constraints=cons)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "uuid": "76321897-4b6e-4714-965a-79bdd489b846"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "     fun: 0.10942155263403677\n",
       "     jac: array([0.11098003, 0.10948556, 0.10939826, 0.10944918])\n",
       " message: 'Optimization terminated successfully.'\n",
       "    nfev: 54\n",
       "     nit: 9\n",
       "    njev: 9\n",
       "  status: 0\n",
       " success: True\n",
       "       x: array([6.50521303e-19, 1.06170603e-03, 5.43263079e-01, 4.55675215e-01])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "optv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "uuid": "031a4259-ecec-4cf4-85cd-98515fe15a6c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.   , 0.001, 0.543, 0.456])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "optv['x'].round(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "uuid": "1859a17c-e501-4a6f-88ae-16b9cf10b308"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.109"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "port_vol(optv['x']).round(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "uuid": "1859a17c-e501-4a6f-88ae-16b9cf10b308"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.06"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "port_ret(optv['x']).round(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5504173645147666"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "port_ret(optv['x']) / port_vol(optv['x'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Efficient Frontier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "uuid": "a49f6ebe-1552-400f-b97f-a26d1bd9fa2a"
   },
   "outputs": [],
   "source": [
    "cons = ({'type': 'eq', 'fun': lambda x:  port_ret(x) - tret},\n",
    "        {'type': 'eq', 'fun': lambda x:  np.sum(x) - 1})  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "uuid": "a49f6ebe-1552-400f-b97f-a26d1bd9fa2a"
   },
   "outputs": [],
   "source": [
    "bnds = tuple((0, 1) for x in weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "uuid": "75433eba-18d3-416a-95a9-c404293ef495"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 2.99 s, sys: 30.6 ms, total: 3.02 s\n",
      "Wall time: 3.05 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "trets = np.linspace(0.05, 0.2, 50)\n",
    "tvols = []\n",
    "for tret in trets:\n",
    "    res = sco.minimize(port_vol, eweights, method='SLSQP',\n",
    "                       bounds=bnds, constraints=cons)  \n",
    "    tvols.append(res['fun'])\n",
    "tvols = np.array(tvols)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "uuid": "b16fdf94-8324-481a-a360-ed2060b9f481"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7fd8818d7690>"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Fl9h8//tw7LEWSllAko9++t/Ur/gIALeumjF/+90d9tut/qiYwsBf/xv1K1ZQMnMmTlnZvlzSfq2v/X7sD/rbXZjdGTztziJ+nfI8LwEc7vt+68iU7/vvtNnkOeCn7CJ4qq5u2pPT9jkVFUVUVtbvesN+QvpjR9IfO+or/WEMvPKK5pYbFAufSxGGGmg/cBrsbOK8oYu46BtVTP/VdwDY2mZRirrPPicK4ym7Kv9TCtpc/x71h07D9COoCYA+0Id7o6/8fuxKjweAAyVhvKvsziJ+u3IZcG/bJzzP+y/f93/S8nAC8ElXNloIIXpTQwM88IDDrfMd/JWdj5gfll7KeQMe53D1POVfO4ph3/1+u9ulpkyiYckbYFmkp0/vjmaL/q5qc2+3oEd1W/C0O4v4eZ6ngJ8Do4GLPc/L+76/sM1h5gLnfuXQFZ7n/RpoAjzgx911DUII0VM++0xx660u99zjdLrOXFo1cHrRAs4pfJBhgY9bOhB74AhG/b+fYaVT7e4z5K//Fw2HH4pVWER62pTuugTRj8m0XRfajUX8DPBvLf/a239WO89d1bWtFEKI3mEMPPd0lvl3FfHn51yM6fgDaLTzGecPfppZUz/ErlpPbt16AILaGgoPP7jDwAniO6GKjj6qy9svxHaSMC6EEKJbNTTAgw86XP//qlnT0HGuiCbk+OLXOCf9AIeNXoeVSjLhxmvY+vCTVN55D86AUgDc4UN6qulCtG9A//odlOBJCCF6yJo1ivnz46m5ujoFtB84ldo1zB60iNnDFjPj72ax5bZthI1QcuIxWOkUgy6/gPyGdTS8vQwVNJFduZzN11/HoO/+FcqWt3XRC6r36H6wPk/+yoQQohsZAy+/bDFvnsPChXanU3MTkyu5YMRTnGAvxDEZEkUV5Dd/wUE3XY3JZnEqBgLxNNzwf/oR1Y89RvUTj0E+T+Oyd6j587OUnXlWT12aEK1k2k4IIcQ+a2qChx5ymDfP4eOPO75rziLP8faznD/uOSY3Po/OgYps0KAtqFnwLOlpUyk87JAd9lNa444ahdpew86YflflWew/JHgSQgix1zZsUMyf73DXXS7V1R1/oJTqas5KPsDs9IMM1JuxnHKipIsK8phsFpVMtG5rjGn3GAWHHkrx108m4/u4w4dTcsqpXX49QuwW1b8CdwmehBBiHxkDS5da3Hyzw1NP2YRhx0HT1PGNzA5v5kT3aayqjSgFaI1pyqATDjgW2rYoOHwmBHnS06fsNOq0nVKKgZde3k1XJcQeKB/c2y3oURI8CSHEXspm4YFrK7n1wYF88Gm6w+0sy3D22QHf/W6eIw4P2Hh1M/VLi8lmqiEIUFqj00kKjz4cZ8hgik84hqJDD6Hpg/epuv9eNvzLP1Ey+1yKjj1+t9tmohCU7nf1d0QvqZGEcSGEEJ3YvFlxxx0O82+I2FY/rsPtSksNV16Z49vfzjN8+PapN82In/4tJh9Q89yLbPvTU4R19ZTPPpPCw2dQecvNbJ3/PtkPjyW/cR3Btm0A1D795G4HT3VPPUrT0tewCosoufQq3BGj9vWShehUf8u3k+BJCCF20/Llmptucnn0UZtcruMRHW9iyJWnr+LUkkWUTR5F2fBTdtpGOTZlZ5xC2Rlfvrbp+usINm9G2Tb1r75MYsyYL7dPJHY6RnuipkaaXn0RopAwm6HxxWdxL//O7l+kEHtBEsaFEEK0CkNYuNDmppscXnut47dMRcQxFe9xXuouDkstx3rdEJSWUPkG6HSKkuOP7fQ8QU01TUtfJ7txI1YigTvuIMovuYzax/+EyQeUzv7qSlUdtMN2UMkEpqkJYwwqkdyj6xVir0jCuBBCiPp6uOceh5tvdvn8844/GNKJPOcfvpK5k16i5N3HyW/aQlAZELkWyrKwiorIr/9il+dreO1VjKWwCuLcqYJDZ5IcPYbkD360R+1WrkvxnMtoWvISurCIom/M2aP9hdgrpYN6uwU9SoInIUS/0Ny8rOWnEzvdbs0axbx5cRXwhoaOpyKGJb7gW5fV8e3/PYyiolFU3l/A5jcDMAZtuWjXJsrlcNJJcutXU3n7bZRfdDFWKl6DzoQhTcvexh4wgMTYgwhrq6GqEssYVLqAwmOO2+trTU2bQWrajL3eX4g9peoqe7sJPUqCJyFEv1BdfSugGDVq5+DJGFiyxOLGGx0WLOi8CvjB9lIuGPgwR6VeZfDg2RQV/TUAA+eeC8aw7U9PocKQ5OSJVFx1GVtvup7sKp/Myo8xQZ5B3/kuAJU3XUfziuUo26Zk1jk0vfoSytKgNVZxMckxY7ulH4ToFjJtJ4QQB5YwrKe29iFAEQTXtD6fy8HD94bc+D/w4dqiDve3yXFyeiEXHbSYEZUvo1WInSyhYelbNLz3AYUzpqG0puKSOVRcMifONVIKEwZEzY1AXJMpt2EDjW8vJTllOplVK+M7lKKIugVPEjbUoYzBRCHusGEga9SJPqS/lcSQv04hxAGvtvZBoqgBgC1b7qGu7jJuv91m3u+zbM2UdrhfmarkbPc+ZqUfoWJAiFNQTr7BxoQQ5TJE+TzBlp2nK7Z/kCjLpuj4E6l7fjFRNkt+3Wqqbr8F15uEXTGI/Mb1YAx2URFEAcayMFFE2RXf6ncfRqJvM5LzJIQQB5bq6ttaf3799Zu4/PLvkskooP070Q6yP+Zc9w6+Zj9FIpFHuQ4jfvGvBJWbqX5yIbl1GzC5HG7FAIpP2rH2UtjcTPO77+COHoM7bDgD5l5EYtgQqu+5g7C+DtIp8p99yuCf/ZKGJa9il5SSnHEI1XfOJ6ytIX3YkSTHHtSNvSFE11N1W3u7CT1KgichxAGluvpuvvjiHzCmqd3Xy8vf5plnvszPaG5O84c/XMeihVdyTPpVLh6zkEmZF4lqa9AOKNvGLimmcelSys46jW1334Hl5CChsQeXoKwvF/2Ncjk2/+435L/YiE4kGfDtvyIxciS1jz9E1NxI1NgAWpOcPBV7wEDKzjm/dd9BP/iH7usUIbpZf6vz1L8yvIQQB7yysssZN+4FXHfSLrddvXoqP/r+i7h/1tx/9r9z7Y+WMnPQKooOmcrQv/0OdnEB2rYw2WaaP/6YsGorytIoOy5DkFvpEzU2th4vt3YN+fXr4nynXJbm5e8SNTVhMlmsklLs8gG4Y8dR8dc/6ncVmcUBTul9+9fH9L0WCyFEJ7ZuVVx77cFcdNGbLFjwzQ63e37BRbz+40v599q/5QdjbmDqmaMZdOUFFEw/CKckQXrCaNxhAwGDMRF2SREqmcQqSKMsG7TCGjAQXVDQekxn2HCs8vL4gVIkxozDHjSY9DHHo9wE7rjxVHz/77CKOk5OF6JP0mrf/vUxMm0nhDggrFqlufa/cjz8RCHZ0AESzJv375x55u3tbn/kA8uxrRUAOKWjGHDeLLbMv43sqlUAbJl/O/nNG9G2ARUSZRspPvFE8uvX0fDWW1glJQz5x5/sMIJkFRQw6G/+nqY3X8cdOYr0zMMAKL/kSsyFl4JldXkieP7Tjwg3rceZMhOrbGCXHluI3WWKK3q7CT1KgichRJ9lDLy0KMs1v6zh5dXjgYIdXp848e0O93UnNBK9U4xTUcqIn/8QnXDjA7YIqrahVAS2AgwmyKK0ZuAVVzLwiis7Pu7Qobhtcpm2U91QeiD/0bs0P30/RBH55W9S+K2/RyVSXX4eIXZF12/r7Sb0KAmehBB9Tj4Pf/qTxbX/0cyH6wcC7Y+4TJ24BIAoownnDSc5YRzh118BN8SaGmBvKMQuSVJ563yimmrK584hqKomrKvHGT2CptdfiRe3AwoOnkFQU03VXbcS1ddTcPRxFH391J665HYF6z6DKAIgqqki3PwF9qhxvdom0U/1wam3fSHBkxCiz6ithTvucJk3z+GLLzSQbne7CrWBc607uXDydURrXfL/NQInGo6VGUSwdAp8ZxVqVCNEAVZxMRhD4/IPKPvG2Yz43z8D4uVTNl93LU3L3yM1fTpDf/Ajqu6+jeynq1BKUff04xQceTS6oLDnOuAr7HGTyK94B5PPoQcMwhoyvNfaIvq3/na3nQRPQoj93tq1iptucrnrdkVzzulwuwlqOefZt3KCtRBLh+jPLXJ/OAiMgyrPkFuzBnIafj0ZPbee5MHTCBsaIDIQhWz+/dVYJSWUX/YX6ESCIT/4ux1PoDr4uZc446egLv4u4cZ1OFMOQbmJ3m6S6Keiou7Pt/M871RgDrAFML7v/+tXXr8FaFsk7WDgUN/313R1WyR4EkLst5Yt0/zuf1ez6M2hRFjtbqOIONp+njnJ25hqv40xCquwAHdoOdYHHkyySQwbQuaj9zG5LDrhYiyHkTOvJv3NadQ8s5Ds56tpWvIiOaXR5eXowiLK516y07mKzz6PsLqasL6OgqOP69VRp+3sYaOxh43u7WaIfk43VHXr8T3PSwM3AFN93896nvew53mn+L6/uM1mi3zfv79l+2Lgtu4InECCJyHEfiaK4Ol7a7n2d4q3Px/OV5PAt0vQzKn2I5yfuovh9tqWu9gUOuVSdsFZ5D79GEyEVVDAkL/8CyrvuouGN99EaYvSs2dRdNQRAJTNOpP1P/sHTCZLpIDaGqJspt1z2iWlVPzN33fPhQvRl3X/tN0xwFrf97Mtj18FzgZag6ftgVOL7wDzu6sxEjwJIfYLmQw89JDD9dc5rPqk4zpIZaqSc5N3c1bifkqcWjAQRz2ABSqpyPkr4p+1JmpsZPO1f8QuLaL83Nl4P/o+dWGbqb8oAqWwiouIGhvRBYWUnD6rey9WiANN96/FOAiob/O4ruW5nXiep4EzgN93V2MkeBJC9KqqKrjtNpd5N1lsrer4LWmUWskc91ZOKXwGV+VRtgJtgTFExsRLqTg2lm0IM40khg4jbKgnrK8jrM1jmooIt20js+ZzGBmnRRhjUIkEJWfOouHVl9GFhQz45ndwBvWvRU6F2Fc9UDF/C9D2W1Vxy3PtORd40vd908Hr+0yCJyFEr1izRvE//5nl/j8VkQ3dDrebYb3G3KK7OKL0PUxdDUoRL5FiKZTrQBSgtcJKapSJwFLYhUmKjjkKHIfaJx8jqKwj2JrBKi1FJ+JRp9wXG6m542bCulrsocNwy4rQrgv5bIdt6W7hus8I167EGj0Ba6QsDiz6jqiw2xPGlwCjPc9LtEzdHQdc53leORD4vl/XZturgMu7szESPAkhetSyt+G/f7KZP68YR2TaT7jWBJyon2ZO6lYmJFaRGDGM1KRDCDMZ8us/J8xkUGEek8+D46BVgLItCOIvmuHWrTQte5Nh//wLGl/8M6a5EPJ5nOHDKZo6lUxlPY0vPEtQuRmA5qWv4gwagrJt6p95jAHf/bt229Wdwk3ryD55F+RzBMvfIHHuVViSCC76CN3YvQnjvu83eZ73feAaz/Mqgfd931/sed5vgCrg1wCe5x0CrPR9v6E72yPBkxCi2xkDz/0ZrrkaliwrYsfR9y+laOBMfT+znTsZWlSJQoFto2xNyhtN0ztvokwzTpGNcpKEDU04gwcRbNoYn0RriEKIQsLqKhreWEJi5CjAoLRF2azZrefSqXQ8badUPOXQywv1hutXQz4XP8jnCTeskeBJ9B3dn/OE7/vPAs9+5bl/+srjd4F3u7stEjwJIbpNPg+PPmJxzX/mWbm+pMPtBqhNnJe8i7NSD1DkNMZ3zmmNUWAXFuAMryDcupmooRGTzUAIVqIUe8QwCo88isSkydQ+/ghBdTWmvgZn8GCUVphMhkF/92MaXnsZZ/AQUlOnt56z+OzzMJkMQW019jEnkP/8M5Tj4o6bQM1Nv0Wl0hSeczFWSVlPdBX2+GkE7y3BNNShC4qxJ0zrkfMK0RV6IOdpvyLBkxCiyzU0wB23aq7/fcjm+vargAOM1iuZm7qVryUXkCwvIKpvigMnC5ShZSoui1NcBBjy27aiVIQ2QKYZd9RIhnzvfwFQdtKJGGPYduetZD5agVMxmOLTz0QnkxSffBoAja++QG7bRsLh40kddiSll+y4Rp0JAqp/+yui5iYAmhY9RtHcq7qji3aiS8tJXvx9ws9XYY2agC4s7pHzCtElemDkaX8iwZMQosts3qz44y+2cMTiU5MAACAASURBVM8zw2jIJjvcbob9BnNT8znMeTmemnMTpCZNoPnddzFREG+kwSkvJWzOkP3sI/ImwC5MxmvNmbDljjjVOvUGoJRi4F98G2MM9U//idp75+N6Uyk8/us0v/c29U8+guNogqVvYpWX444d/5WWGUwYfPkojLq4hzqnC4vRUw7r0XMK0RWiwvLebkKP6tbgaVel1Fu2uQj4D+CHvu8/2eb5NcCalocbfN+/vOX5McAvgE+AMcA/dHdimBCic599prj2Wpf77rXIB+0vTKsJOd5ZxBz3FialPopzjZTGADptM/zH36Ppg4+ovP1ucF3S0zxULkfz+8vQ+WZMEIDWWOUDMJlmsCzShx7aGji11fTaSzS+tBilFLlPVuGMGEWwZROGOKE8CgOCLZt2Cp6U7ZD62plklr6EShWQPunMLu8rIQ5EurGmt5vQo7oteNqdUuqe540FKoF17RziNt/3f9XO8zcAv/R9f6nneT8AfkocTAkheti772r++19qWPTWMEwHi70laOY06xEuKLqd4amNKA0mgO0FWJSjsGxoWvERqYNGMeY3/0p6WpybFNTWsPqqK4gaWip+K8Wgv/kByfETIMjjDBvR7jmj+trWn00YENVUkz7qODLvv4OpqsQdPpLkzCPa3Td97Emkjz1pr/pDiH5Lpu26zO6UUl8NrPY87/+0s/+Jnuf9E/FtOc/4vv+a53kO8HXgzTbHnIcET0L0GGPgxRc0v/+PHK+9W0ZHy6cUU81s+y5m2XdT6tbipDTaaUkq1QpCg3JstKPRyQTBus/YuvhpsCxKzjiLsnPPxy4pJTltOk1vLQUU1oAB2AUFuIOHdNrG9PEn0/TW6wTr1mCVD8AZPxGrsJiBP/wZpU5ETWijdPtr5Qkh9oIkjHeZ3S6l3oGftYwupYF3PM/7BtAINLepGrpbxywrS2PbB/YbZUVFx8tZ9EfSHzvqiv4IQ3j4YfjPX0e8s0zTUdA0WK1njnsrp9oPk7Qy6JSN5aYhysZfTpVCGcDWFB1+MEF1LcMvm0vd0iU4LQUszeqVDBxYiAkC1EVzWFdfTVhTg1NSytAjZuCWdn49pjxFY6FLOGxwfL6XF1DxF99pfb0764cbY4ga69HJFMp2dr3DfkD+XnYk/bHnooKeuSt1f9GdwdOelFLfie/7S1v+2+R53rvE1UTvAVKe56mWAGq3jlld3bQn7e5zKiqKqKys3/WG/YT0x472tT8yGbj7pmau/YPF+voBQPvfMMfqj7nIvZkT7IVYKozvmHMt7OIUTsUAwuZ6TE19PF9nKwqPPpJRv/lPALTjUPvpp+Qqt8XLrWyq5N1vf4egclMccDXUYVAENqx77AmKZ53XaZtNLkeuoQkiAENDdV1rH3Tn74cxhmDRA4SrP0IXFGGfdhF6yMhuOVdXkb+XHR0o/dHTAaBuqt31RgeQ7gye9qSU+g48zzsFcHzfX9Dy1HjgU9/3857nPQ8cASxtOeZT3XgNQvRb9fVw660u1/8+ZFtDx2M1BztvcFFqPkckX8dYFia0wCi0bbDSLloZwtpqrJRDVJyCfB5laaLKL8hvWE9izFgABn3/b6h7dhFRLkfDwicItlVi8vl4qs8YlK0hlyW3/nNq7ryRqHobiakzKDjl7J3apFyX1NFfI/PmK6hUAanjTt7j6zfGkF/6PGbbZqzxU7EnHrzrfWqrCD9bgdIa01RP+NFb+33wJESX0JLz1CV2p5S653kK+DkwGrjY87y87/sLiUeTfuV53qHAMOBh3/dfaTn094Bfep53OjAK+HF3XYMQ/dHWrYqbbrK55UZNfXP7a84pIo5xFnNx0XwmJ5bHwUIYoe0Iq0Bj7GRcITMMMCFYdgKyzS132IFVVIhVVEDDqy+3Bk/aTVB69mzChgbq/3Q/mAhM1FIBvKUUgTGoIEdu5ScopWh6YRHu1Bk4Q3ZOHC849WzSJ58VT9vtRTJr8N4S8q/Hd+yFqz9GDRyKVV7R6T4qlYYgwDTXg+VAWqZ/RD+hJOepy+yqlHrL1Nu/tfxru81y4IIOjrkG+HZXt1WI/m79esV117ncfbdDc3P7wYZNjpOdJ5hbcCuj3dXxt00FxkSgQNlxQjm5ACttEeUMaNB2GC/mqxUkXCzXAqWwB+4cjFiFhSQmTSL74QqMk0WZsCX4MVjlZbijx9D8xedAy3nbrJve/PIi8v4H6NJyCs69HOXsfc6Rqa9pDbpMPoep2Qa7CJ7MlvVxn2gd90dJ/6p9I/oxudtOCNGf+L7ij3+weeRPCYKg/TfAJI3MSjzABek7GGhtIa5KEAdO2/9DQqGt+NunO3E8Yc1WrKYGCEOUVq2FDJRtYZUPoPQb51B82hk7nCeoqiTz7tsUn3UOmaHDyG1cT37Fuy2jUEAYkDr2ZMKtWwirq0hMPhhnaDzqFGzeQOblZ1FAuHkjmZcXkTp55ym93WVPP4rw04+I6qqwRk3AGj1hl/uY+lp0IoFKJuPinZnGvT6/EH1JVFDa203oURI8CdFPLVum+f1vLRYsdDEdJIEXqRrOde/kHOduiqzaODhqEwihiQMjV6FbRluskhLGXv2fKNel8rb51C9eiNq+4C2gXZuK7/0NBYccusO5wsYGam6+Jq7RZNkUX3wVRQMHUfl/fkzUGCfwOoOHYpeVU/rNv95h3+yy18mvWoHJNqMSKYAdKoXvDV06gOSVP4TmJkgX7tbaXdo7BLPmI6It69Flg1BT2q8lJcSBRjdLwrgQ4gBlDCxZYvG737m8+GLHf/4D1CYuTN/KrMJHSKkmwlwECRt74AAs140LTzZsRdvx0JOybayiApzBQ3CHDcMuLaX+xcWE6z7F0iE4CiITT9UVFbaOULUVrFtDWFsV118KA/KrV5GYOIXU9EPIbViHtjRF512y0365D94ms+gRAJQJMek0dsVQksefts/9pSwb9mCNOWXZ2LOuxAR5sOy9yrUSok+SnCchxIHGGHjuOYvf/kbz5rKO15wbbq3m4oL5nFr0JK4VlwE3aCytsAeWUnbWaZSfP5v1v/hnwsiOp6aIq4RrbUhPm8bAb30H5Tg0LnkFogilbRQBtJRaU1GILtw5kdoePQ5rwCDCqq0oN4E7YTLKtkkdfSJ6+dskjzmJxMSpO15XGBCsXhlfoFLxkipnzMGdPKMru2+P9ZX6TkJ0mX72RUGCJyEOYFEUF7b8v/83zfvvd1wo9iD9IRcnb+L4oudx7LD17rY4n0mhCxIkRw7FLUuz9drfEdXWoGwbFbRMjW2/C+6j9yGbgaIirKJiwuoqdFkZUdVWFAZlOxR87VQSYw/aqQ1WKk3ZX/2IzHtv44weiztyLJnXX6D5uSfBQPa5RtyDvHg0CDC5LI333Uh+7SpoaEAVFmOPHIszfnKX96MQYhekwrgQoq8LAnj0UZs//MFl5UpoHfb5iunOm1ySvplDrVfiNeYKCjHZpjb54HEQZZUmSYwYRONbS+NSA6UlRLW1LXe7GbQdr09n6mvYdtMfGfSTX1B+xbeoW/AkaE3RabPIrfkUZ/gI3A7WowOwikooOP7LmkzhF+viNigIt23GNDagiuPE1Lz/PuGm9VjJNMZNYk+eSXrWXBn1EaIXRKmS3m5Cj5LgSYgDSDYL99/v8Mc/uqxd2/E3wSPcl7gsfTNTE8taKn5rtKMwVohVaEM+jDdUoBMancuQefcdsCyU66Icl5JZZ9P44rOQaUZpg0KhCgsItm0hbKjHHlhB+RXfaj2nU9H5bf7tsQ+aRH7lB5ggxBo+GtUm/8iqGBYHSmEASuOOn9xlgZMJ8pg3FmKaG1ETZ6JHTeyS4wpxoNKZDuteH5AkeBLiANDcDDf/agM3PTyCLXUd5zQdn36Oy4pvZIL9ISY0YEBZoFyF5VooO0DbGhJ269RdFERxLmgYgFKYpkYoUkQ1VVipFCbKxWvVATTWk5g+E6skHh0yxtC85EWimiqShx+LNXAQ2Xdfx+TzJA8/HmV1vuZk4uAjsMoGEm7djDvtsB3ueLOGDCd19sUEn3yENXQkzpSZ+9SHbZm3nsOsej++3sovMEPHoJz2C4YKIZCEcSFE39HYCLff7nDNr3NUZSa1u40m4CT7aS4qmMdBZWvi+o0qLuRo8nHUoxxAG4jiiTrVZqkFZes4n8Gy0K4DOLhDhhBlm7ErBhE01sUlC2wHXVCAtqFx0RMUnHEOzS8sovH5p1FKk/t4Oe74ieTeezOehlv7KYUX7brerT1yLPbIse2+5ngH43i7XjZlT5ls85cJsLkMBDmQ4EmIjknCuBBif1dfD/Pnu9xwg8O2bRrYebTJJsdpzqPMdecxVK/HKlBYjhOPNKEwGJSK/6ttHU/ftTMQpJMJSr5xHlF1FbnP12BymTgpfFsGXViILhuAyTYRlxqPCDespWndGuxBQ8h88BbRtkqwLMLGeqIv1kKYR5eUE25a393dtNfU1CMxWzdCphE1bjoqVdjbTRJivyY5T0KI/VZtLdx8s8tNN7nU1LT/TS9BM2e6D3JB6lYGWVswJsIq1NgpC9UmCTwefWKHO+ss14EowtBSNdzSFBxzHIP/6vutx2/+6EPq7ruFYPNGTNZGWwZVWAhRCGG+ZStD89KXCD71ifJ5yGZQTQ2QdDFRSEg17vTDuq2fOhNUfkFU1YAuH9LhNnrgMMyc78XV0SUBXYhd0tn63m5Cj5LgSYg+oKoKbrzRZd48l/r6jpZQaWJ26h7OL7iNcqpoiZRwCmzspA0qznFqXQtOgXY0xph4Wi6dIlFRQb5yE9p20MkUhaeczoArrmo9R1hXQ/PLC4hqqyCbwWSaQCt0qgBdPoCothoSKVQ+Q7hpHWSb0a4NWKggH69vZ1lY4yZScN4VHV6viaJ4usxN7lZl790VvfMiNR8uwQQR0fRj0Id9vcNtldJg9688DiH2lkGm7YQQ+4mtWxXXX+8wf75DY2P7H+RpVc+5qXuYU3AnJaoGlQBt2aAhCgx22t4+1hQHUEphACdpx/FVS66CVTEAq6wca0A5qcnTSB96GOmDv0zCDrZWUjP/GvJrPsXkcuiCQqL6WqzCYqKmRmioI3XU8RRf/lfU3/5Hwg1roSBN1NCA0hqVTIDWKDdJwflXdhgURdkMuT/dSrT1C/Sg4STO+1aXJWubz/2WRXsN5vOV0Enw1K7qLehlf4Z8jmjCYTBuepe0a39nbVuHtW0txkmSHz0TdOeJ/qIfkoRxIURv27pVcd11DvPnuzQ1tf+NrlDVcn76Ts5J3U2JFQ+ZKxusVMsHWwR2kYrf06L4KaU1lqvB0mil4srcLaK6GtwhFViOg1teAo31mCDfOm2VXfEupqEOXVhEWLUtru9UXIw9oIIwXUBiygyKL/tLlFK4E6fRvGEtWltY5eWodJqophoKirAci9xjt6POuBD7oCk7XVf4wVKiLRtQShFtWkfwwZs4M4/bo/6LPv0As+FT1KAR6EltpgcLSzCN1fF1F+55job6cAmqphIA/eFrRGOnHvgfGkEOd+07qCiI+81yyI/q3QruYj90oP8dfIUET0LsR7YHTbfc4tDc3P6bUbGq5oL07ZyTupcC3YhVqOMpugi0q1GWah1N0k58DKOiOKfJ1ijV8nqbwAmAII/K5wlrq6l//AFUIkHDM48w8Oe/RieSOGPHg+OiATVqDMWXfpv8h++R/2wlzriJFF/y7XhdOiB57MnY4zyyb7xA/sN3oLkJXVKKVVCIUmCyGYL3l7YbPOmSAV/euaM0unTAHvVhtOlzzGtPxblbaz4kSqTRY+Oq4/pr55P+ZCkNDRmYccIeHTduT5tA9gCuqGxtW4duriUoHwWW3VKmgngJnCDb280T+6EwufOSSwcyCZ6E2A9UViqu/aPFrfMdmnPt/1mW6m3MLbiVb6TuJ0UzADoB2o0X58XwZWAE0PLZHpceiB/ESeJxmQJlRfHadaFBaY0zZmw82pPLxrfmRwH59U3UPXgHpVf8Fe6osZRc9pfkPvkY5yAPq6ycxFlzUG6i3fbaQ4Zjzb6U+lUfEDXUolwH8llwE3GeVUH7b7bW+Kk4x55OtHEt1vCxWGPbL8HQoeotEIYtAaWB2q2tLynHpeDEs2iq3LvkVnPwCURBHpXPEXmHHpDftq2ta0iseQcAe9vnNE89laBiDPa2dRg3RX6IFAwVO9PZht5uQo/aq+DJ87xS3/druroxQvQ3lZWK665zmT9P05xt/8+xTG/l4sJ5zEo/RFJl4ieteBTJTusvi1lG5stkcA3a0ijASlrxNsZgAG1ZQIS27Xj0yVFY5QOp+Mef07R4AcGGteRWfYSJQrTrYhq/DDTcgzycseNpvO9mmj5biVVSRnrut7CHdLLkSiqBtgYBoAYMQg8cgk6mcE+c1eE+zqEnwKGdjwxF1ZXw2pNxYvmkI9CTD4/PMf5gzCfvw9aNUDoQJhzS6XH2SGEZ5sQLMLvess+yGqpaf1bZJlRzPfkxh5EfdUgcLPazej5iNx2AXyQ6s1vBk+d5E4DBtH6X5YfABd3VKCEOdJWbQ377k83c89xBHY40letKLi6ezzeKHsaNmlrLByhHoV2NndJxvaaWoEnbCr19KkkDlo12QKuWvCcUUQSWawEKE0YoN4EzYhTFs+eSGDaSxJXfBaB63jVk31kCroszceoO7Qo3fk5+9UqUbRM11pN79w3sM9sPnpTW6GGjCVb7KKVxJh2Ce+RJXdCDwHsvQdXmlp9fxkw8BGXZKMdFn/1NaKyDdFHrQsJ7JJ+Lg4R+WKYgKB2GVbUOFQZEBWWYgrhavCSJi071s6B6l+8qnufdBpwMrAFaFrxifPc1SYgDV1UVXH+9y03/Y2gOvXa3KdeVXFx4C7MKH6SgMAAgyrXUZFIKbSmshEZv/zBTBhMZlGOjki6O1fJnqi3U4GGYjZ+3HFm1BFgKpW2wDZEJYesXZN9/k/RxX2ud8kt4kwk/eAOCDLlFjxAdfSI6lY6PUjoAlUpDLocxBl02EBMGBCveRqWL0AOHkH36bqL1n6GLy7BPmIU9YTqqqAR79ISu68y2b9bxbYNfPtQWFJXt1WH1qrfQK98CrQmnnYAZOXlfW9qnRKVDyEz+OrqxmrB0mARNYvdoCZ6+aiow2vf91pFqz/Mu7L4mCXHgqa2FG25wufFGl4aG9t9kynUll5TO5xtFD+HqLErFU28AKhmPMlkVA6C+Js5vahlNUijcqVNJjh9PtGUjuZUr4srhxqCjAJNOooI8uEkKzjyPzKJHMUEIBiwNRAG5D5ZhmhpRBYUYY8i/+0acN6Q1UUMtzU8/gE4XYFUMwTnseArOvYL8h8vQAwaROPJEso/dTrh2VZxQnExiNq+Pb+dvbiR483lSV/2k6zv1sJMhl4VsM0w+sjVZfV+pNR/EBT+jEL1mOeH+Ejzls6hMPaagrNsDGpMqJkwV73pDIVqEif5VhX93gqc3gCKg7ZLJ/SvEFGIv1dfHFcGvv96htrb9nIBya0vrSFMqEcQDKKql8nfrgEpLpaYwhz1sOPkvNrY+pxMuBVMmU3bZX7Dtut/GdZyMQTlunG8UpAkzTShtCD5+n8TMo8guXwaZpi//koMsKpmi+fmnyC9/k6i25su78WyHYNUHaMchHxmwHdxDjsY5KE7kNlFE9MXnraNWpr7my1EgY0B3z30purAUTru06w+cSEGmMW67m+r64+8FVb+VhP8KKtdMVFxBdsrXZURI7Fd0rqm3m9CjduddbQaw2vO8j4Es8dvteODB7myYEH1ZQwPc/MeAa691qMu1fzdaqd7GpUXzmF32EAmdRdkKjPoy6bt1jZQ4Z0nbFooIu7gIXTAe09yACg26pBh70GDqHrqbYNsWrNJSlOtS/p0fkHn9RZqXvoQyBowh3LyexKQp2KfMovH5J7GjKJ7xKiggrKok8/ICaKwHrbFGj0UXFGONGEPkvwvEAV1UtSVuXhgSvvtKvIRJ+SCiTevicggTDyb8Yh1s24QeMAT3a9/o9v7uSuEhp2GteBm9ZQ2qZjOseIVw6vG73M9a+z72+o8wdpL8lBMwReVd1iZ765q4RIDW6LpKVMM2TPGgLjv+bjMR9tbP0EGWfNkoTD+7PV10QhLGd5IC5nzluR92Q1uE6POam2H+LRbXXA3VTe1/sBTrai4ums/s1H2krAxaKbSj0HbLUiktUZO2VMvdcfGbkpNysIrSqHwzhcefQvGpp9H48gtYxSUUnXomVdf/NyrIo3PNqGwjDQ/dhj1gAE5xMfnKLfHddrks2TdfwRlYQWLYKKLKjShtoYqKyH/0PjTUxTV9jEE7LiV//S+YIKCpoYZw/Wp0cRnOtCMAyC9+mHDlcgD0yHFYx56OKijEnnxo67WqvphEWlwOhcWo2iSYEGvtB4RjpkNBJ0U1wwBrzXtxIJltxlrzLsH0k7usSVGqpDWYNm6y14IWZ8sqnG1rQCl0YxWZg47rdx+aon2mL/6t74PdCZ7uAap9339/+xOe533QfU0Sou/J5eDOeXmu/reQbUFFu9sU6Vrmlt7O+SX3kNZNcX0lpVC2QtkWSpnWQEk7Gm3FwVQUKezyQqxcFu3aWIVpUuPH4Q4einvhl9NWzojRNL/+UjxjZmnMpvUEdVVo28JKp4kMqDCPTqcxDTWYTBPKstAlZejCYuyRY9Al5ZiGWtAae+RYAJRtk774fxFVb0UXl7bWdTLVlV9O1dVWkTj3W93Ywz3McuNpO6Uwtr3ru+6Uiqcnw7Blv64NKMLB48kZg26uIxgwqtemE1WuqXVKVuUzcW6YJcGTAOMW9HYTetTuBE//DLzW9gnf97d1T3OE6FvCEO69oZar/zvFxob2K2GnVT0XFt/BBWV3U2jFheRag6YEOEk3nqkL4rvktK3Rtm5JClfYtsLKZgCDaWrCFJWgC4sxUYTJNNO89BWCTRvIvf92vAhvEMZVvE2EtiysVJoojLBKyloW6k1ATS1WIgluEtKFFJx3Oc7YiSRPmU1u2RJUKo1dWkLmtquhoAj3zIuxBg7e4br0yPEEWzeBMdgjD9q7Dsw0weoVUD4IBo/eu2PsJbXpM6y1H4CbJJh6YtwXLULvSMhnUJkGomEeJNKdH0xbBBOPwlr3IcZJEkw4sosbqwiHTmy93bm3hCVDsRqrUGGesGRot+Wzib5H5SXn6ate9H3/9bZPeJ73Dd/3n+ymNgmx3zMGnnzS5t9/FfHpuvZrHKVUI3NK7uSC9B0U2XVx0crtyd8adEJhuw7KTaDCuCSBtttUCN8+Cm7FVcF1Ko3RNvagQTQ+eT8N992CyTYR1VTHd8k1N6Edp2XqD1R5BVb5ABKlJSRmHguhwZk0nfx7b5Bdsrj1jjx3ykycidMASBx9MomjT8Y0NdB862/iXKmGWoI3FuOeumNpN+fYM9AjxkEQoPe0CjhAkIfF90LN1rgmU1EZjJkMR8/q/poxUYj90auoXAaMwbJswoPbTLNZDuGMU/bskIPHEQ0e18UN3b+ExUNoTpehgiwmUdTvavuIjpkemL71PO9U4jSiLYDxff9fv/K6An7Q8nAMUOr7/re7oy27Ezx95nne/cCfiRPGAa4AJHgS/Y4x8NxzFv/x7y7vL2//z8dVGc4vu49LB9xGqVODiQwmsr7MYdJxvSXLteIPH5OPp4cU8V1y2z+QLNBKoxI2VjqNtm10YRE61wzGENVsxeRb9m1uhmQKlc9iJW1wE+iEg9JQfMxxZMZMx2zZgFVQ8P/Ze+84O67y/v/9nDNz23atdtWbVY5ly02yjW3csHEAOwQSSuj1mwD5QSAJgS8BQoAApgVMyBdCgIROCGBMcTAYY2Mb9y7bGllWLyvtanu5ZWbO748zd/eudqW9kmUZ2fN+vaTdnTtzZu7s3t3Pfcrnwbvo+WROOp3S7b9Fsjlyz7li6pMQcSNdosiJsZrOLhtWiDfci7TMQi9+Ar5NQ31ulEq56Ma2jAzA1kdh4QpYNL0H1lEjjl1tF7jnWv08ZWa8LNabvgki5RnMkyykjTEF4MvAyUEQlIwxPzLGXBoEwW9qdnsN0B8EwTeTY06dYc0O4AJcReEtQRB013s99YinVwO/As6r2bag3hOkpDxduP12zcc+luGOO6Z/2WgqXN7wI14396t0ZHtQ2s2Qs7FFKYXSrrYJ4mQwL4gG0c4ZXLJ5wthCuYjnaUSUiz5lMnhNjcRD/Yg0EO7bg9fW7pwE4hjxPCyC39EJURn6elw+sbebeGyE3mt/DPbH4GfQHXPJv/Kv3MfLX0Z4902Et/0Kve4iVM2sOck34J/3fMJH70EVmvDOuQxw4i76328T790BotHPuhS95pwju6FNbdAyG7p3uq/9jHu+XubI1jscPJ9o6anoHY+4tN0JZzz550xJeTrz5EeezgW2BUFQDeLcClwB1IqnVwO/NMb8NTAX+OrBFkuiWN8CduJ+88w3xrz2ADF2UOoRTx8NguDLB5x0mreqKSlPT9avFz78d2PcdN/0heCKiOc2/JzXNH6Jhc278PIeWEG0SgbxMj5rDoWzI4DEw0nG/ZxsWCHTPhsqZezIsIuOIOiGBqhUUFjo70EQov79SFxBsj5k8jS+8OV47bMZ/fn3sbnCuNeSyuWh5FJTks0RdXcRbduEt+IkKjf+jOhRNwA27tpB9uVvm/S8vNPOwTvtAGFULroOPREgxu7eCkcqnjwfnvtKePwh2LMFbAxzl8K8ZUe23mESr1hHvHxtmnpKSTkKxJkZ6gKfOJ1A7UTvwWRbLUuA5iAIPmKMWYUTUquDIJiuXPBNwOrqnF5jTBvwJSaLsYMyo3g6UDglHIO3hikpTy1btwqfvNLnxz/2sUzvnnth4Ve8ofXfWJLdjOQEP5upac9PDJuqhpcJIoIlGeJb+2bNWte2RzzR0dTchIRl8L1kXYtg0XEpSTdVkIbZSFgms2Yd0d7dlH59tRNunoLKGLptLlFYAUDlC8ic+x6WZwAAIABJREFU+e50g701xpZ9k1OGByOTRbV1Eu/fAwiq8+ADgesi3whrznX/jgEy1EuldyPit2Ob2p+ewqkyhte/C5tpcEXdKSnHAKmMPdmn2Icz7K7SnGyrZRBn7E0QBBuNMc3AItx4uQPZXhVOyf59xpid9V5MPbPtvj7N5mcBV9d7kpSU44l9+4TPfS7DN7/hUQmnD0Wfnb+ZN3V+EdOwAWJQGY1SetLfYkvNyDUL6KQGXIHESdG4Uk5i2WQ2nYqQcgWb9cHLk52/gHBkCH92J9HenTA26lJySTW5xSJxiL/yZESE7OlnE/72J5BPalIaG1n0oc/QddsdxPt24ZlT0E1u0KtefjKVru0QhuilJ9blySSiUJe/Fnn0bqSpFbV8zZHd5KcAGerFv/86QgnxrUfl9OcdVSPLI6JSJLv1HiQsErYtIpy76omtF0fktt/j3J5FKEdlwlnHtosx5RnKk5+2uw1YYozJJqm7ZwP/zxgzCwiDIBjERY1OAEiEkwa6DrLeYmPMC3HpPwucz2GUJNWTtlsEfDv53AdOB66t9wQpKccLQ0Pwufft46s/nE8xnj64uiZ3H/9n9uc5rel+PF+DaKTW58ZORJuUuDSdn9NIUvsEFn/hEmSk3xVJg6tb0hoaGhHrok6q0AAixMNDqEoRqRTxF59APDwEpRL0drm0nlJ4J6zCX+KsAlRDM9LYjB3odbPrFixDZXP4J6+Fk9dOei7eqeegFi3HFsdQcxfVfZ9UNgenz+y4/YeG6t2FRGXwFBKVUb27iJ5i8eTv2YAe7gER/L0biNoXY/3czAceBAnLqNIIqMQvbGzgaF1qSsohsU/y1LYgCEaNMW8DvmCM6QYeDILgN8aYTwG9wJXAJ4FPGWP+AVgOvD4IguJBlnwf8B1cPbfFiajX1Xs99YinNwVBsKN2gzHmynpPkJLyh06pBP/1Xz6f+7Sid3B6v6Jlmcf4i44vcE7D7wDQflLMLZNdtK3IeHTJy6iJrjUSz6ZlK/FmzybesB+0Hhdbas584oE+yOVgdBg8n8Llf0a0/i7igT4nrqIKs973ScrBg4x87dOJ6PJRaqJLT/IF8q/8K8p33YQM9KB8Te8Pvo694MXINEaPqs3VcdkoxBZHodDoCtWnwW5ZD+tvA+3DWZchHXW8SRsbQh66BeIQe+I50NoB5RKy/WFobMXOPXat/XH7AuyO9UCI9TLE7X8AfS+Ton1P/I+P9bPEhRbU2CBWKaLG6ev0UlKONsfCqiAIgl8Dvz5g23tqPh8A3lLnWtuA840xjcnXw8aYuvPc9YgnMcYsTj5XwDwmd96lpByXxDFcfbXHJz6RZfv26V/4c7xdvHHWv3FZ2y/R4gq4q8XfNraTa5k8N4PO86prCeLrJAigIJen8z3/yPB//ydFJVBJ2uM9jRodQGU1Xvss4qYGxPOp/PanMDwAcYxtmY03dyGiNOEN1+Aplw+Mo5D48fWMffbv0KtOw3/en+MtXYVoTfln38BWipRG+qFhFt7Z0/sWxX37sDf8jxvNsmAZ6tKXTy+gHrgZRpN6zQdvhktfMeM9lvtuQO3bBoAdHSK++BXo265GBly0JVpzPnbZaTOuczSwjbOonPECCuUeRjKzsQ2tx+S8h6Iy90RUeRSpFAlnLXpCUScARFFcfBZ6cA9xpglbOMRImZSUo4j1n/SC8aOCMaYlCIIBY8yFB2wHN3ruJdMeeAD1iKeHgP24t0UW2AN8qs6LPKShVbLPy4FPAO+sGm8aY84C3gXcBxjgziAI/iN57MtArSPfO4IgeKie60lJqXLLLZoPfzjLAw9MP5m+VfXymvav8MLWH5L1K+isRtBOOHlJGi4MiUOLeG6civaSoiZbLQbX+K2tiI3Agrd8FVRCyhsfBrHjQ3+V7yGeh2puJe7vRXfMwY4Nw8B+175vLZL1afjz/4ONY6iUET+DDStupAsxDPUTbVqPmtWJOv8F7klMCmQcIqoR3OuEE8D2Tdh9u5A506TxagVVvYXWlZqIeXkMyqPIYM9EQXzPnmMmngBsQyv+0kXY7qGZdz4W+FlKy49ysbzSRK1PsJA/JeUwkfBg2bE/OO5OtMl3gccOeGxFvYvUI54+FATB5w/nyqA+QytjzDKgG9hxwOHzgKuCILjTGOMD+4wxVwdB0AN0BUHw1sO9npQUgA0bFB/5SIbrr59+VlleRnhZ2zd5Ree3aPSLbqxJRjt38Jqok7MX0OiMOB8n7dJ4rgDconwPz5yEVopo13ZssUi07XEGrvonVGkEEYiVgOehs1kkX0Blc8RxYkqptTOmtDaZM3cCKu/e2al5i7BRCMODiLUoGzoxVikS73wcG4VIWzv6hJOxvfvIzp9HuPbCaZ8v4AbeJnPcyOagsXn6/dZeAg//HrQHZ9Q39NYuPx374O8gColPOB0yBWzz7PHIk52ddoOlpDwdOI4GA68KgsAaY/4pCIJJPlDGmP9T7yL1iKdJlerGmDcAC4Ig+NgMx81oaBUEwRZgizHmQ7UHBkHw0wPWCoFK8nmTMeb9ybYR4MtBEKT2wCmHpKtLuPJjmu//IEtsp6akNBVe3P5D3jDva8zKuu5VURrQSYouTvSFJB10SRtd1b+ppvZJKYX2FGzdRNzURDw2ggDKhtj+/a5USglkPKShCVmwlOzCJaA1uXMuJty8Aas9KrdeR7R3F5LJkD1vIuWWffEbCe+7FfIF4oFe7L03wcgQSoD+bsIf/bsb7htV0OYMZr3k1XQfItIia54FUYgd6EGWnYwqNENpDDLZSdEmWbQSFh2mo/hCQzx/hRNn2v26ic7906TmqQ0799h4OqWkpDy5HIuap6NBEARJVw/barcbY16H0xV1UY94Og/4fs2J/8sYc1DXzhrqMbSqh7cDH08KwcBVxz8YBEGYVNm/D/jooRZoayvgedOnZ54udHQ0zbzTM4jq/Rgagg//9S7+7VsdFKPpO+gubv4VfzHniyxp3JUUdzvjyklvpLSgxP1DKURrrIDOiDPEzOdd5KkSIsoiWjs/p5EhvKwPUYTYqJqpQ5SglWbRez5EbtkKKnu2oxqb8do7GOzezOiD92DLI2SXLEW0R75nG23nPCu5mCZY+GIA+n7wNUrNzYRjg87/SYHt2YXX0IhVHrJzIzaOmeVXKN7/e6Shify6C8aL2Me57HIAbBgyfO13iLp2oFvbKfzxa9GF6T2ujpwmWHDRUV7z8EhfL5NJ78dk0vtxBHhPsF7v2PNCaorPgyD4pjHmm8B/1XPwQcWTMea3uMqNlcaYWjMXTX1tIfUYWh0SY8yrgIYgCP65ui0IgntrdrkBeC8ziKe+vqf3tOeOjqZDRhaeaXR0NLFnzxDf+Y7myo8K+wen76o6pXAfb5vzOU5ueAjlJ7Pmqqm5RFzEcexa/jN6fJuIYNva8YqDSBSDVkghT8OlV1DZ10XlgTsgTNJvohKbggjRkkSdkgHBShgYC+n94XeINj7kOuqyOezOx7HlEogirlSQttmMZZoJu4eId28h3rIB6ZiPXnUa5V07nRt5pYItlwnDEBavwvZ3oSol4kyOyp4d9P/yh26WnI0Z3t+PrEvSbmHFRYSqSnHLemT7ZhAh3NdF8fabobEZ2bcD2zYXVq1Ddj+GDPQQL1oNjU990fXhkr5eJpPej8k8Xe7HMReAUWnmff4AMMb8J07bPOsAH0vNUap5+qfk4zuBq2q2F4EH61i7HkOrg5LkHhuDIPhnY8wpQClxDP10EAR/n+y2EthUx7WkPIO49kdD/M27hY1bp+/+WJTdylvnXMUFLTehcwoRD6Xd7DmYKP9xQ3wVyGTnbdEKLxx10RuxiALVUKDhgueiZ3dS2ryR0W/9K7ZcwhZLLtJUThaNrdMpSWSq+D//gRKQTNYN+925GQlDJ7gAyebwn/18vNPPIx7oJfzVD6BScp4qSiFzF2N3Pu4u2vNAK/Ta85HfXQNao/INFO+52XXtgUvDDfa6/e+4Ftm1CfJN2PNfDM2zoLHNiak4mWYQltEP3OhGp+zeRDzUi9690S21MyC6+FWuqD0lJeUZzZPt83QUuTH5uAi4qWZ7Ebi53kUOKp6CILgJwBjzYBAEfYd7dfUYWhljBHg/bh7NnxtjKkEQXGeMeRHwWeA+Y8yLgXbgHcBGoCPxmRrFdeL97eFeW8rTk40bFf/4fy033DJ9mqnN28+b5nyZP26/Bk9ClKcmokkuW+c+T/4b/6gn9lNaIZ64iE11Z6VQNmbstt/S+MI/J1p/FxKHSEMTcRQ5oRRX3EniCJQgotwIFa2xIwPgJwXs2RzEIUQxoj28teeTOdMVe0dd27H93QgWyTVge/bgXfpnVPZuw+7ajFKCaB+ZfwLSPgeKo2CtG/g7/wTYHjihs/hEGOhGtj7izBT79yHXfweWrMaedhH2jOe4WXNtne75D/chNsJqH9m/a/x+yuggDPdB25wj+4aVi6i+3cQtnZA72qnBlJSUY8lxVPP0DQBjzK1BEEwKvhhj6g6l11Pz1G6M+Qnuz8QLgP8G3h4EwdY6LnImQysL/HPyr3afa4BpDUqCIHhDHdec8gxi/37hkx+Db32vQBRNffeTlSKv7PwWr+r8JgU96rrhPHHWAgdiJyJPIgIa/GyGOI6dr5N2heQidnx0nVKCHRsmfOhuhscGCe+7DVsqIqPDTgQ1Nrni6zhGsllyL30z8SN3E3fvQWlN3LEA76QzkEITki9QufEabKWMf8YF+BfWzODesxkVlrFR5OwLTliDiMJ74RuJr/8BDO6HU85Ft84mPvdyZ0GQK9Bw4QsY7RuDfTuh0Iw0tcLYsBNSUYgM90NURrauJ8Zi110Gy0+DOEb/9rvjVgsSx9g5S+Dxe5BS0Y02aW4/sm9auUj2vmuRsSFsJk/5lOc+9aNSUlJSjpzjp9sOgCAINhlj5uKcyKt/DI6qz9OHgY8Arw6CYMQY82bg48Cbj+B6U1KOGqUSfPUrms9eCcOV6VN0z2v7OW+Z9290ZibK7UQLXsYN2o1jJ4JEC0or4ihGaUH73ni0CdxAXX/pCtTsDhgeovLYI1ApuTompdAtbdjiMOFdvwMbu98jcYRqaMJrm0VcLJI59xK8U8+BrRuImltgW0AcVfCWrCRz7mVIkv7yzOmAneoIPjYGrR3IaL+rnXr499j2F6OaZ6H+bLJ7h1q4Aha69L34GURKMGfxxA75RuyZfwRbHkZKo1Bocr/8ShPDPdUjtyJ9e5K5fBrb0gENTSg/61KGCqR7+xG5hOuebcjYkHNgrxTRPdsIj0Px5HVvwhvswno5SgtOBS9NYaY8QznOCsaNMW8B/gpoAx4HDsscrR7xtDVJt70UIAiCvcaYw07jpaQcLayFX/7S40Mf0GzdMf0fq9Ma7uUdC/6FEwuPTrQ3aEH7iY1ANWqkxaXvfO0ycH7i6ZS8i3LRJk3mlNPxGwrEe3dBNoc2q4h2bgUrqNkdiGjini43O80tjDS3IY0NEIV4VGDrI8T9e4l2b4XefUipiPZ92N9F+ODtaC3Y4UHkpHWoWXOnPCe18hSinY+hwgrkG2DHY9hH7kROOULD/yWrXarugRuRLeuxmRx2xekTj48OQraAtTHEEdFJ56OGe5FyEas1oJDicPVWTkGGetDd24laOrHtk38vxS1zsH4GCSugFFHz8TdGRMqj+Ps3O/+v8ih+9+NU5q1+qi8rJeUpwYbHR8F4DeuCIDjNGPO5IAj+xhijgE/Xe3A94mmeMSZP8ucmGdVymGYvKSlHhyBQfOADGW66aXqTy/mZnfzVwi9wyewbESxRxLgYEi8Z1ktiFZBJ7ARwY1aSUXXOvslzx7iOObAbH6CSyARnY+BsCwQgquCdsJywe8eED78Ihf/vA9htm4ju+x1S9GFshKhnD5JvcKk3cEqwUoY9m4n27kBEYXdvRl7yNkRPfnmqFae6mTK3/twVh1sLIwNw+y/cOTsXwuLVBy/gthZ13/XIvu3Yxlbis/8YMlnsaRdjV5/jCsVrzmkXGNi/yxlbLlyFXXIS6ubvAhYpjREXmogXnTTtqWR0kMyD1yNhGW+XonTSxZMElG1opbzmUnTPdqKWOVPE1XGDlQlxfnxlLVJSjirHS81TDfuTj3mAIAjipKGtLuoRT98CHgHyxpiLcF5NLz/cq0xJeSIMDMCnPunz9a9niOKpL9IGNczr532Nl3X+NxldQWlBUKBctKkWlfXRSWedCIit+aun3EZVM8xXRMBGE95I1aIocAXV/d3Yh3pRWrCRdQXhHZ14szqwxWHi4jB2sA9pbIGGZsgWwNvvirV9H7XUIIXGcUNKOzwI5RLkp748ZeVp2P5u6NoGrbNRe7e4mqXRQfBz0Pw77IlngTlzkhACYN92ZPujzj6hOIp67G7ik58NY8PojXe5WXPmbHd9gF2wgnD2fCiOQPNsKI8hlZLryrPWpesOPEf1Ng50uX1FXO3UwD7CAwSSbekkbDkS67eDYGPUwF5stgGbP4hL+lHEZgpUOlbgDe7B+jkqs+vuck5JedpxHHXbVVmTaJqupK67l8MIDNUjnu7B2QycgXtv9fsgCHqP5EpTUg6XKIL/+mwPn/rSHPpGpubUFREv7vgxb5r3FdoyVWfwCfGjDyhiFBG8jILIuuiSkmQUnXXj5pRMSkNJ1UVcaWdJoJ2FAHGyg018m6yAVk4QKUVm3fmI9gjvvAE839XChCHegrmwezPkc5BvcI7el70cdj5GtGszlMZQS06E3PQ1XCKCnH0ZDPXC7s3Iro1QKbnIU1hB9e6G9bcQ9+7Bnv+nkw/2M+76kidok/oc74HfIL173MbSCNFZNUXq2cK4mCKTJ567AtX1OGQLRAunSVFZi7fzYWRsEJvJuRRfJkfUsXjqvkcTa8luvgM91I1VmvLC04hmPfnRrHD2MsLZqUt6SspxGHl6MxDhbJX+FtfV/8p6D65HPO0D3lJt70tJOVbcfrvmvW8d5tHd0/9xWtt4F+9a/BmWFzbj5TVY7fyZLEnqDHQSvbHWorVG+zoxqGRcFCGutokkRSfKRaxcCk8Qr8amQJLCcqWRbAFKoyitIay4x/IF1MpT8Nc+m/C67xPv2ea2t7UjuYITTsUxiCpQKSI7A7jretQ5z4OXLISRQWT23AlfqZ2b4M5rwc/Cs18Ms+ZAzy7U76+BcglLVH0iybw9l3qTwZ6ptUiz5hGbc5C9m6FxFnblWre9ODIRSSuOHPwbIkK45mJY9SwnBqeJOnlb7sXb9SiIEGcbCJetJWqdC/kn2bAvLKOG97uomrXowa5jIp5SUlISdPapvoLD5X+BrwZB8CXgysM9uB7xdMOBwskYY4IgCA73ZCkp9bB7e4V/+oDiJ79sAqZGYOZmdvPXS67iOe03Ir6g0OMpNalNp2U0OjFsksS0SWn3hY3jZD5dsnvivYRS0DYLNTyA2DgRUZIUSLuUHCJorZG2dtSis4g2PYxk88jiE9BRBW/dhdjf/5J45yYY7kXiGArNsPYCuP06JvwQFCiNHeiB7l2o5lnQMX/iiYZl579UGnFpshu+Dy99J+za5OqkRBA/S3z25W6dTfei+7udGGyf3lXdmjOx5kykdzdqywMutVZohLEhUAq78MQpx0h/F2qol2iBccOKs9NHxQBkbHBciEl5jKhzKejp69MmLiqeNEPviPB8bKaAlEeBmDiXjtdISTmmVJtljh/KiXAaxxijgiCID3ZALXWJJ2PMX+H8mqrl9P8XeONhXWZKygxUKvDF92/nqm8tYzSa+gc6q4q8fv43eNWC71DIlFHaS6JMsfM9Uorxqm8SnaOTFJ4FNBMiy9NYYjfUFxeZIldAzWqn8MJXEz16P5W7bnR5Q6Xwz7oY9m7D7tmKWMD30ctPQo30oWa1OR+n7p2IUkQ3/QxbaERGBlFYJ8gqRaShBU6/APvIXTA2gmQyoH1ksAeu+xbkG+Hil0D7PPcERoehUnSfiyBjw3Dntcjux2F0AArN2GwB5i13AmjZGqJdj6G2PYw0NmPLYy7VNjqE2nQvtnkWtnMpavdjeI/cjAz3ItYVb4eLTiRaeTZk85PuuRfchv/4HUgcE2++m+KFrwEEb/M96L5dzqfJz2KbZlNefSHR7EXo/i6IQuLZCw4tnKwls/lO9KCrUyqufLar25r2h6OE7t9FXGjFNkxT0ymK0gnPwtu/lThTIGpfevDzpqSkHHWOw7TdtcaYU4IgeKhm2+eBv67n4HrE00eAvcDf12xrIxVPKUeR227TvOddlmDLydM+fln7dbx98ReZk92HaFDaGx+wa0PQWc+lrWC8g07pxJZgmroncGtIEkkSP4M+aS1eLgOP3InX0AyXvBC7ZzveSWvxCgXCoX0wZ4HrdMs3oma1w+5N7nw9XZDLQyaHLY+hTzmXeM8WCEtOPIkgYRn97Cvg/D/GWovduwOGelF3/hK0hvIYbHnYeTk9egeUi9jZC5F920EUdu5i9K7H3PPJ5IhmL4BTL3LCKUHv3YLq74L+LtTQfsKzrqB4wzV4fftd2u3kC1D9XUgcuYiYta7QujhMdIBwAtC7AyQpkFfDvUhxBIpDeHs2OIfw0ig2W8BWSuiuTUTzDaWmTiiPYWcoBleDe/H6dgKCjPTjd22ksujUqTtGIbnHb3XnUprS4rXELVNdzW22gcr86X9+UlJSnlzscWaSCbwJ+GAyAaWEe9vdxlEUT98IguBttRuMMe863KtMSZmOvXti3v+2Xn76++nrmlY2bORvl3yWM5rvdxsSwTTe2GEtytMoT0/q9RAtU7bBAWm9qqjRCrExum83+B5W+8Q9Xfinn0vmivdSueFqwgdvgcE+KI1h/SyqsQV55E7s4H7INbguunwDtuwKvvW6C5BTzsJ+7yoY7of2uagtD8LGe+DEdcjJ5yJzF0Nzq0uDVZKgbsts5L4bUFsfdgIklyd+3utcNKpnJ9z/W7dfJgdL10wZjSLd25GRPpeCG8wgo4PEg/snUml9XcRtc1F7Hne1UXGEVZpo9qLpv0GFJhjpdTVMXgabLSDF4erNrL2x4waRttDs0pQzYL0cNqlRcl9PXzOhRvtQpZGknilGD++bVjylpKQ8hejjziB2J3BxzdfCxEzfGZlRPB0onJJtn6/3BCkp0xGG8NUvxXzqkxmGy1OFU6Me4q1LvsxL5l+NtjExuG64xH/JlTIJyhO8rEccJU7hSpzrd1VfaQ+i0C2adM4hid+T4GqarEVlfNi/FyuCbWjCZnMQxUSP3kP04O+hUkZsjPU8NytucD80NbsicM9DP+dPUSvWuGLwQiMigs4W4A3vw9oYuenHbl4cwKN3wuqzXf1QoRkueBFs2wBtHdA+BzbdA8UhJCwjlSLs2EC89GRobCXu24v078O2zXOeTpNuagVVGXNiJIoQBbbQgm7rJOrZh1WauH0hdv4KKpkcMtCDzeSguQN7kPl0pbUvJPPgr5HyCOWV57naqrZ5hPNXo/t2E+fGiAvNxE2dRB1LD+tnwDa0Ull4qkvH5ZoJ566adr+40EqcKaAqRawIceEIR8KkpKQ8adio8lRfwuHyvCAIRms3GGPqzqjVE3lKSTmq3HWX4t3vVDy6aWqaCOCKzl/w9qX/RnumdzzS5HvuR1U8wfOSDjlr0b4GC15WYW1ibklibun5qAWLiXZvQ8IQpdwwXuUrrM4g7Z3o5jbX0RZHrr5JC1IeQ4VF7HAf4eaH3GPFMeeHWGhEcnns2Ihzlm5oho4FaHM6dv8eWH+bK15edwmSc+7isnd7kh6zExGa2qjNnCXu37ZH0Lf+GEZHIEyKLzM5V4QNLnW39rKDOnojCltodYIxtsSdS0Frspe8jNEH78U2z8bOcvVUtnUu/o71yOgAtqWDcsulTswdiJ+hvO6KKZvDE9YRsq6O7/ahCecsJ5yz/NA7aZ/SCeei+3cS59uIj0M38pSUpzvHW83TgcIp2XbQX68HkoqnlGPGwAB89MOab357+m6tlQ2P8Z6Vn+X0lgcBiGOLUk7saK1dp1zS9CbiuuPGTSxlwlqA6kcboQZ60L7CKt/NYtMK8XykZRb+xVeQOfMiij/4d6L1dzhrAz+pg9IebN3gBFiuQFwcc1GrbA5aO9DnPR92bHJRrDXPck7ft/wUBnomol3PfiHc8D1kfxf4GWz7POf5tPrsabvLVNcWiF3hOjbGer4TYvNmEBdVtCZcfR5623pXE7XqHLduNke89JRJu3q7N6CGXTpO+rrQ+7YQzf3DNXm02QLhnOkjUykpKU89x6FJ5hMiFU8pTzrWwjXXeLz/fT7d+6f+yDXoYd665Cu8dOHV+DqmWtDkaT/plhNnSVB1+K4ttakZ3jupngmBrI+Oy4inwUs66pRL6aniEPb+m4nnLyH/irdR+o9u7N6dLvpkQfysc/Betpr4nhuRjI+0tqOUQj//lUhTK5x8NjxyJ/zuJ64rbjBx+/ezzi9p/25k/x4X0RkdQjwfe8YlML9mkO5IP/rR2wGIs/mJ+p+ORcRnPc+NY2mt34XbzltOWIfYsrV2A6KIs40H3zklJSVlBo63yNMT5YjEkzHm00EQ/P3Me6Y809m2Tfj7t4fceMf0vjsv6LyOdyz7Ah25PhfxqQoc5WbHqYxGtIybXk6bsxKSKFQyyBdBZTVe7VgWEVQSqQKQKMTu2U543feIL30pdO9GsJDJQKEJiUpI/15U5lT0ec8jvvc3YEPItU1u59/6MBBDaSy5ECCsuKG7zbMh1wjD/cjoEHgaue83xIVmmO38nPQDNyK9uwFQLZ3Epz0HGRskXnaqS+3N5JF0hERzVyKlUWR4P3HbAmzb1EHEKSkpKfUiT9LvqicTY8wKYCnwW2B+EAQ76j32oOLJGBMz/Z+qKql4SjkolQp8+csZPvOZDGNjU8O5i/Pbed+qT3NW271IRtDKvfCq3ktKu0648WiTBWvjRChJIrCcYBIEXxseAAAgAElEQVQleL6HVD2bcOm+qlCyJIXkKNAaiZOhvFGI3bcD+4N/RYjdiJY4RJWGXHArrMDvr4XTL0CJuNqn+UuQTE1XWKEJ+rtBacTzkGwOvAx2/nLIFbAX/Cnc9Ut3nfkGiEMY7B4XT+M+TpUSqnsrks0RrrkQvfUB9M5HQGeonHQ+dm6dqbvDIFxy2hQbh5SUlJQjIa425hwnGGPeAHwQ2Ar8DvicMeYnQRB8u57jDxVn+1wQBBo38+WPcJOH88nn738C15zyNOeeexSXng8f/Wh2inDypMJfLPs6//2sN3DWrHsRDToROkoLWntuDAou8gRJfZMSVDaD+B46n8HPZdAZPW5TUHX+liTCVCsKlLh1x4WXiPNV8n1UJovY0KXylDrA3sC6iNLOwBWKN7W6GXC3XAN3/Qr274Fzr4CVZ8Ap5zo7As9zaz50k1uifR5c9DLoWABxTNzSOalLLl52GtbLuC457aF6d6E33Ibe8xiCIFEFb1di5m/rrmU8JF7XY+Tv/Sm5+3+B6t9zVNZMSUl5ZmNFPaF/TwEX4AYBbwyCoBwEwUuBc+s9+KCRpyAI/i759LQgCK6qeeg3xpiXHdGlpjytGR2FK6/M8pV/94jt1BfD2tb7eP/qT3NCYzUyqphcY+jSXkqpqSHPRFzh+biAkkVE4WV04jJuXSedpxEbO+sCrBNL2p1HPB8656MXLHOiqHuXi/zEEdgKSSU6EwPycDPj9u914szPwsgAsn+nK/jetRF76avgrMvcrj073bkAKY1NPId8I/Elr3Z1UPnGSV1tdvFqonnLUTd+G0lafQWc99PoIFhLLJC542qoFInmrSJaPkOXW3nMXZ8/vW+Sv3uDs0EA/F2PUmqdd+j1UlJSUmbgOCwY7wqCIDbG1G6razQL1FfztNIYc3oQBPcDGGPWAqmNb8okrv/Pjbz3nxeyY2hqbVOLN8A7l3+RF86/Fs+bLKrEVy41F+O01ETNN5Jxj7lCcEk8nNyjNrSuForENDMGNasDicqoSgWJw6RMStz4FgTV0Ogcx/fvgoUrUWsvJN66wRlXDvW7lB4WRLvBvUrhZXzn/aQ0eD7iaye84gjGRmDfDmia5UazRBUYG8TmW4gXrnJ2A4lxJNqDhpbpb56fIVp5FnrbQ1g/R7jyLLAWb+sDWD+LhCVksBsAb+fDRIvXHFQYedsewNu1AZSismwt0TQ2AFb7zj8KnFt6SkpKyhPkOHQY7zDGvApoNcachcuqTTP7aXrq+c35fuDnxphmXPnIIPDKI7nSlKcfQ0Pw/jfs4Ps3Tx8NuXzO//I3K7/I7MYhlPiu481a0ILyFNrTyTiVaj24dSm6RDRpX+PG11m3r+dSc7GnndCqrqcE1T7HDbjt3evWICnaUxk48Qx0FMJIv7uwwf3IrE703b/C5gtu+K7W4GWRzgUuctPfDaURxFoEi21uQcaGkShy56yUkP4uuLsL2b8LIYamViSsoB+7A7v9IcIz/ghmzRzZiZeeMsVOIDz1EgC8DbeOe0RZ7U/vx5TgdW9J7kuMt2/ztOKptGwtmV2PglKUl5wx47WlpKSkzISS4+6N2HuBq4DnJv/+lzpHs0B9DuO/M8YsA07E/X3bEATBcTc+OeXoc/31mne/O8fu3SdNeWxebg8fPPGTnDv3XhftsckffAs66yfpNYu1LrXm3MDB892PpI0mEnfa126/Gk8npXEz46zraxA/g4wNYsslavsc3HuhGNnxKOSbnSjyPGTBcieOwgriZ9xgX0CyGezK05FTL0B+/S3U1kfARljlocRCHCKeIs7kwdOoLQ85X6bhfucWbmOkNAL5BqRcRO/YQDSdeLIxVMougjTDO7Zw+ZkQVZBykWiBcVGsg2AzeaRSAmux/vQmpLa5k1Jz/fYHKSkpKTMRVRtxjhOCIOgDXnekx88onowxArwamIObOPwS4HtHesKU45/93TH/8I4Rrr5h/pTHhJg/X/Rj3rHiKzTly64DTVzkyMbg5TxX4J2EmrzMRCF3tTsuWQhbtSawVdNLXJcdgHIdeaISsaW0izQVGmF4gHEBpXBF5XEMuTzx/OWok85GzV+KDSvJzLhd48N1JZdHtj2CXXOeq5FqbHUdcsql68S6lLiKI5CMm7c2NoQQYeOQuKndpffAGV3mp/FPGhsi8+D1zpKgdR6V05472TQzqiClUWy+2QkrP0t48sV1fW/Kq87D2/EwaI/K4mmG7KakpKQ8CRxvNU/GmHnAF4Dn4P5g/BZ4ZxAEdXXR1BNn+wzQCTQBnwLmGGM+HgTBPxzZJaccz/z615p3vVXoHpoqnJYWtvGPp3ySMzsfAWS8a646YkV0VfBUu+jUNKIpEUdVt28t2DhRUCRBGqXdMVUbg2wO1ZqIluIYNpNJIlKx67IDd3yliFq2GjV/qVtLe9jz/8QVcj96B2rvNrdrWIY4xs6ah/TuBSy2dQ6yb6t7XGlQ1o1mIUaNDLuITzZHbM6GXANqZ4AtNBGvnJrO9HZtGB+5ovp2IT07sB1L3DUN9ZJ59EakNELcOo/yyZdMPM86sLkmKivPqXv/lJSUlKPB8SaegP8EfgVciUtSXJxse349B9cjniQIgtcaY76UzH35vDHms0d4sSnHKUND8MEPZvnud6dOztYS8fpl3+Nt5pvk/BDRGqWVS7UhLkVXHeZbtQvA1Tcd7PXmrAuqXXIqSeupiYycJOLJ86GtA3X6BUilSNy9C79vL3EYQrkIWrk0lue7qNKSic4KuefX6G2PYP0c8cozXMSqOOyiUeUx7KkXErV0QKUEy08l2t+Fvv0nyGAPkm+EqIyELkUmURlbGkF1PU68aDXR6Zce9F7aXOPEnDvlQW6iyF7v24Qk3XKqbw8y1I1t7nRi8BC1TikpKSlPJUoddzVPe4Mg+Jear+82xqyp9+B6nm21da+2e3x2vSdIOf655RbNO9+ZY8eOqREQ07yJj6z9DCe1bESSVFy12FspNR51GicRUYDzY6q6ikNiNaBcRCiKJnyZwKXpVDIQOI7BzyLP+TNEa3RrB6JBurahL3kJba0F9j/4AMxbitpwF+zcmJxbufErPVtgsAfZ4fyTpDjkCr7nLEQ23Yvs3YK95UdE574IltbUc3UsID73RXh3/gJshAztd09HuUHEElXw+vdgB/dSAeycZdPez2jBiVAuIqN9xO2LsE2zJlJ12UaqOU3rZwAht/5XSGmUqG0e5ROeVbexpYwN4vXvIoo7QbXXdczRRsb60SP7ibONxE1znpJrSElJefI53mqegB5jTFMQBEMAxpgmoCv5/C+DIPjKoQ6uRzyNGmO+4tYzfw9cBtz5BC865ThgbAw+8t4iX/v+1Cn2WiL+cuW3ecvq7+KrCKwiCiO0ryaJHqUVk8JLlsTeSRAt6KRAXBKhVR1Joto6XEE3OK8l7bruREBpDYuW4+3bCns2OyfwSslFoh66Bf7y/ag1Sepq9VlJ19wonHAK7NiAXn+Lq0caGURshMQRsnODSweWi+4iRzxU1xbipsmdq3b2QqKV65C9m9GVxLIgjlzLv+e7tKO1qMFuooOIJ0SITpjocpORPrLBzS5V19xJuPhUGBsm6liC17cTVRwCwOvZTmXOKmxjHd20UYXcljuRsESlbyt67slEsxbPfNzRpDJGZm+A2BCGoCxC3JgWqqekPB05DtN2FwE7jDEPJ1+fBDxijPktzjzzCYunDwFvBNqAZwHfD4Lg60d+vSnHA/fco3j7WxSPb58qnE5o3MrH117JKbM3uZom18iP9hUq401+CSW2A9ZaEIvyJgrEVU0EpTpCRVcfL49CNsukgKfghJTSSM8O6Nk22dASoFykeO/NqM2PQrlMvGodXPEml/YShdz2M8bNMD0PrGB1ztklxHFSc+Xqo+La4bk1xCvPhBNOR9/2Q+jbDbFAvpk404AKS8R+jrjzIMJpGrzuLROpusF9VBacRJwUe9ux/hqbAg/8XF1rquIQUnFrCqBH+4+5eFKlESSujEfKVGmEOJ0/nJLytOQ4FE/bgb+bZrsAfzPTwfWIp7WJWPo6gDHmT4wxfxQEwa8O6zJTjguiCD7/eTeTLoomvxiEmNed8EPesfrr5Lwygh6PFklDM9kTT4VtjxIVR7ClcLybbjz1hnURJsBNBoonjk+68sYdvuPQ+S7VzEsadxD3fCeGphtXIopwW4AM9IAIev3NRCef65y9Ads+D/ZugdFh51ju58DPOSPMfKPzbbIxUmjG37WBSs0olVq8Lfch5TE330hprOdDSwfleSuwLXPGzzctlTK6Zwu20ErcMoe4pubJehlsfuLrcP5qpFJGysNEsxZhDyLoDiTOtxDnWlDFQdAeYfOxH/wbF9qcoCwPY3WWqDHN9qekPF2x9rgTT/cBOgiCGw58wBjz+EwH1yOeXg/cU/P174Av46rUU55G7NgW89ZXDHPX4wumPLawsIePrvskZ3U8hFhBnNU34ntIJoPX0Y6UR5Co6ASOr0EpbFQ7X7rmxdXaiowOITrxbkKBn4FkbIhkfPA8bKgRIldHhWBtnLiAK6wkBpkNLdDQCuUROPv5qMfvJq4KNmthbNiJmbCCHuhKRpNUULGCSkTc0Ey4+BRobEZtfxhGBtyx4SHszEIXUbEiiI2ROMZmsjMP8I0jchtuRI0NYEVRXrqOaM4KKnGEjA0kAqlGeImisvQIjCyVprjiPPRgF/mFC4hHnoJfbEpTnn8qUhrC+oUJt/WUlJSnHVo/+Q0txpjnAn8G7ANsEAQfPuDxNwBvBZIRCnwtCIJvHWS5vwC+P90DQRDsmG57LQcVT8aYf0w+PbvmcwANLJxp4ZTji2uu8fjbd8BQcapwetmyX/Cedd+gsQlk1McmXkfkGvBaW51YGh7A7u+qEUMOqfoOVL9WrkhcVp+JevAWJ4S0IErhxuH5SDaDsiFiI/AEqEkFiu8iUvkG5/S9dDWccznq9p8iwx5231ayF/4xlZ9/G6mUiOcsgVwBfftPkd7dSFRBqAowd4FSHCG74WaIQheB8jLYfDPxrPlOJHn+lHsSLjkF1bvTGXOKT9ixhLAOiwApj6HG+pN0mkUP7iXqWEo4/8Q6v1MzI6UR/J4tzkG8YyWq0AwjQ0dt/cNCaWy+9ak5d0pKyjEjjOoeC3dEGGMKuMDNyUEQlIwxPzLGXBoEwW8O2PUVQRBsrWPJW4BJESZjzOuDIPhGPddzqMiT1Hysfds6Cry9nsVT/vAZHoYPfGB6C4L2bB8fO+cqLpp7BzKrk8yKVVTuvx0J3dw33dyAv+pkwkfuwRZHkPE5dCCeTuqKFMRJN131P89Hd21BWlqxo8Mo5SwN8DQ0FJA4hHKSrkscyBHlnLWbWuHcK9wsurZOWHYy8vCtyOiwK/ju2+tqqc5+Hiq4ExWXsL/8D1R5xF2HgG1ohfKYczj3/STCFAEWsRaIEULU3sfQwz2U114+dZZcrhHxs26uHSCZLGRmrkeymTxxvhk1NoQVRdQ0tabsiZLZsx5dHHZRt6gC884/6udISUlJqeUY1DydC2wLgqCUfH0rcAVwoHh6uzGmCygAXwyCoPcg6w0BNxtjbgSqa14OPDHxVA2HGWP+NwiCtLvuach99wlv+8sMm7dNFU4XLH2YT7/+eloevw9CUJSxG+7ByyjIZFCisOVRZNEy1I7HoDKWzFRzwqlWSFllJ8wvlaCUIL27nQDTE9pcwNU6VUqTrsUCks3BohORc18ANkbveBi6N2PDYtIRV7Us91Cts5EH7nDdd6VR9Nigi1YllgJx61zssjOwDc2QbcBffyMM7pt46YfONoBKEUYH0FsfIFp59tQbGE0UQxNW6rvpSlM88Tl43Zux+Raitqlmo08UVU03iiBROkkpJSXlyecYiKdOnOCpMphsq+Um4BdBEHQbYy4H/gc4mOnec4FvJp/LAR9npJ6ap3XGmHcEQfBaAGPMl4F/CYJgY70nSfnDwlr49y9rPvrhDJV48o+Ar8q8+9Sv8eY3jpGd00Glp8Flj8uj4/uoxKxRRGBrgNZA1gcLcRSNO4dXkXG7Aoto5Qq/q+k7pZLBvgrxPWwmg0gMcU1BuJ+FM58L654LgL7jZ0hSlySb7iF+3puJKyXo34edtxw9qxPyTc7LKaxglefSdIBtmUN0wcvHu/T0pruwza3EYwPoqujwvKQgPZmjN9TDFAcTEaIFJ6J3PQLaJ1w4db7fQfGzhPOnL0Q/GlRa5uP3bgXRhC1T07ApKSkpRxvvMCYhHCH7cJNOqjQn28YJgmBLzZc3AD81xuggCKYzoXp3EARX124wxlxX78XUI57+CHhTzdcfwo1peX29J0n5w2FwEN75zhy/+MXUOp7lTdv4zDmfYM3cnXC/oqIU48Xe1fSZVuPDeRHBbgvQURmbvHAUNaaYIs4dXARpbIVKGRWWxqM11QgVTNRCqUrRGWcqD6IYCk2QbyRuqTF5HBtGxoax2TxWF9x1LD990nOJTrsE+9hdqN7dqMEebLmIzeSpXPTq8fN7j95MZsu9YC1xNkPc1IaEZdfRFpZdZElnIDd951y4aE0imqRu48pjQdixnLBt0USqMyUlJeVJphJN0/18dLkNWGKMySapu2cD/88YMwsIgyAYNMZ8AvhgEAQhzqtpy0GEEwcKp4SzgNvruZh6frMGyfTh6hd7jTH7DnVAlZkq45N9Xg58AjeQ7+c1218DnIErRnk8CIJ/T7YvBT4IbAKWAn8XBMFwPdfzTOehhxRvelOebdumvkN4xfKf897TvkJDQ4iX8ccH8NrqWDkRJ250cmxSx0RxBDydxJVA+R7KUyhVKyjEFV03tSID+1Bip4oNm9QbVaNRoog7FyGFRtRAD/re67Cb7yeedwJqqA+IoVwkOuv5TBqqW8XziVefRwzIvm2o7u1ES04ZHwAMoPuS+Y8iqCikeNJFrkMw3wxhGW/nw+BlqKyYJmVX5cBzxxH+zgdR5THCWQuPvTFllbSzLSUl5RgSP8lpuyAIRo0xbwO+YIzpBh4MguA3xphPAb24GXVdwJeMMVuAU4DXHmw9Y8yJwL/gRJbGpUfagH+t53rqEU/LjDFrgiBYn5zwFJxoOST1VMYbY5YB3cCOA45dCLwbOCMIAmuMucsYc0MQBI8la/5jEAR3GmPeAbwXJ6ZSDoK18M1v+nzgA1lKpck/4E3+MB8/67Nctvg2lBa8TAYmJqi4Lriki6Lqs+TWTIq8axClUL5OCsNrR7IAftJFp6obEpRyvkqJFhNRSaG5j+SbnA1AWIQoQnp2oUYHAAuZLDosozbeSUX7Bx2FgrX4ezagevfg9e2kfOL52NmLAAg7l6EHupLIUwNxxyLwJgrDK7MOvx7J7wrw92+H2NkijDXMrtubKSUlJeV45ViYZAZB8Gvg1wdse0/N51cdxnIfBP4ReBvwEWAJ8Ip6D65HPH0clzecjQsu9AB/WsdxM1bGJ/nJLcaYDx1w7POAe5JBxODCdS8wxmwFngPcVbPmV0nF00EZHoZ3vxN+/LOpnWBr2h/jXy/+JIub9iKSmWIzUEWSKJLO+Ek0KknhVQWPVuNpPJHqGuNqyLVrlkeQyjAw8Vi1+0605yJcjS2uSFu7GiUZcuNZJAqTzrESqhgjngdxhNUeUhnDf/xuygcRT1IcRvXtcTVVUQXdvZUwEU/RyrMpNrS4USqLTkb37EAPdBE3tBIuOPnIUnFhGamMIVEFrMXbvZ7KskNErlJSUlKeDhx/JpnbgiC42xgzFATBNmCbMeZF9R48o3gKguABY8wqoGpEsyHJJ85EPZXxh3vsbGCsRlTVtWZbWwHPe3pPpO/oaJqybeNGeNELimzYPFU4vebEa/mHM79Kzg9ddCkp5sYyUaitnEASrVAZPxFMiXDKZpH2uejiYDIPDmxsaxzCXZpZPI32faeUotitKco5e2c8dL4RKkU34LeplbhSdseWRiGuYJWA9l39kUrEWSbnBusCUimi8jlaDnj+1fthwxyl5lYojmBjS37uXLyOJmwUQrkEp65DRIh6u6gED7lBM8N78Tpm4y1cedD7HQ8PuDRmoXny9sbTKe/b6Ea2ZLLkKdM6zffmWDPdz8czmfR+TCa9H5NJ78fh4+knvWD8aLPUGNMANBhjXoxL/V1Q78EziidjjACvAeYAnwdeBnyvjrVnrIyf4dgVBxy7CRf1yhtjJBFQda3Z1zc60y7HNR0dTXR3TzZBvP56zVvepBkqThZOBW+Mj533Rf5k2U2uYFt7aM/90LtU3ATiaZSnsaJc9El72MY2ZLAXyfro0jBScQXg1lpECZLLJRGbGFWT2LOQzKbT2MZmpLEFtX83tlwErbHZArbXfStF7ER8ymrsrDmoof1umK9S2ChybuOioVwi6tlN+IOrCBesJlx5Dh2dzZPuh6y8EN31GDbfzHDrCmTrdrIbb0VKo8StcymZ89Hde8mWK+NdeGP7egiz04808fc8irdvEwCVuScSzpkssjIdy/H6doMIFa+Jwe6nyKAyYbqfj2cy6f2YTHo/JvN0uR/HWgAeg4Lxo801OLH0WeAnwCzgXfUeXE/a7jO46E4TrstujjHm40EQ/MMMx81YGX+IY68D3lEjks4F/jUIgkoy8fgs4M5kzV/U8RyeMVgLX/i85uNX5rB28juBVa3b+OKlV7KiZTco7eqbgOqgXqx1FgEwkYLTCq1c15Zt7cBWyojnAkiUx8bXlvGC8mTenVVI1YncWqenfI3yMxCOIYMlYt+DOHaeUHEZRION/n/23jzMsqus9/+stadzTs3VXT2kO92ZdxIIEAjIGJDBH4MDl/sgEUQBERHkMimKKMMNXiKDgPeKwRF5AEWNgvcXfioCCsRACAkhiclOyNRzumsezrCHtX5/rF1n6PH0UJ1U1/t5nvN07X323mftVbu6vvW+7/q+nfongNoQxcR2zFkXQdrAjm/Cm96LntrlPJ3qs86TqVkQ3nMj/oEHaQ0PE9qA7MKnYatD2KFxCi9uF777B+5Hpw2XipzZi16Yoli/nWLyIfTiFLY2Qr7pyFEnb3ZPWxb6s3sOEU/ptsspauPOzmDd9hP6PgqCIKwmVltvuyRJvti1eTFAHMfH6K/VoR/xpJIkeXUcx39cCplPxHH8sT4GdszK+DKq9R5codYr4jjOkiT5lyRJdsVx/FHg43EcF8CflcXi4PrWvDeO458AtgHv6Pdmz3SWluDtb6/wpS8dakPw0vO/wQef/ikGKpnzaWrbCdCuc9KBB/iuQFyVVgKqrB4PI3RrydXy+J7zJNAe5F2rQH0fyr5zyuSduiilXPSqrI1SpUDTWnc1CqaMTC17LFnn2F0ZgMERirjT+sRseyzB7V9DLcyAv9hpHmwteuEAVhs8q2HH7aTx0/F33UGw5y4UkG26EOtFLJtq2iDARgOgPVqXPKe0JwiOWu9kw5pLKwImrB56gNIUE0coYBcEQTgDOR0F46eSOI494Lm4rNryL6Kfx9kzHZN+xNNyw5rumFxf7dH7qIy3wAfL18Hnfg743GH2P0iv75QA7Nih+MWf09x5b69w0qrg3U/+S1536T/hV3y0H2LyojSm7AgntMJbXknne1hjnJFl2RpFpc2OjQDLdgLKpdEMoLrMM411/kLLNlHWOquCMHLu4Uq7Am7avuBA2WSXZT8pj2JwHLvpfIoLrnBjXK7F8gOyy1/ovrzv+wT3/KfzZwqidnE7xrp6KcCf2eV62qV1ovtvohhYRz4wBtEg+brtndVwSh12ib9qLeLN7aOojWIH19Pa/iSCh51HbLbp1PWkEwRBWK2stsgT8P/iSn/ug7YPct99e/sRT/U4jv8EiOM4/g3gBbiUmfAo4ZvfhP/20hrTM71pupFogf/zvI/wrK23o7ygbTOgQ78sEsf1gwsjlzazTsoordG1GgrTcdrWqt1+ZVnEKAUojT33UvSBnc5OQFs8uhpELptpDo6RXflKoq/9mfNzstb9pRJWMEqjlMaMb3HWAUWGDSPU6HrwFMEDt5CPbyW8/2ZUkZKPbEaFFYqRDeTnP4n83CcQ3HcTqrGADUIClVMYj2y7M860YQ3d2ulavyiNTusQVmlc+LRjT27WovLg95w4U4rW2Y/HDG0k2/LYk/22CYIgnDGswjVZQ0mSPKN7RxzHz+335H7E0/uA1+LMo34M+CLwF8czQmHluO46n7e+FdK0VzjF4zv4sxddw7aR/YBGe16n1xwaHfguQKM8VOij07xT76RBYdCeQin3iLiaJtdKxZiuIGRtEJ7/85h9DxB8869LW4HyvWUncaWxrTrhtz7X7m8HCoWimNhO/pSfRtXnIWsS3PQPKA/IW9j5h7F5w7VROfCAS8+ZnGDHbTA4jrf/PlpegB3dRNYlhMKJIea6Cj5b5z4Fb2qnsxAox26CYzfxBdCNmXZRvLIWb3EaM7Sxr3MFQRDWCulhfbwf1fxbHMfnJ0lyX9e+i3BtXY5JP1YFNo7jz+KiTdbtSuwxThNWGGvhE58I+dCHokPee/H53+HjL/hjBiotrPFKu4GyIFwpvChEe64eyVNApYYaHMZ6ASzOopTBM3mn7kd7tBNsiva5VAZg/RbwA7zdCdp2is076TjAGjSmbWnQ3u352A3bIYywaoTo5m+glAU0VitXN9WYxfiRa+yL83xqp/usxVucIh89/Kq4NmGF9LwnE+xNIGtgRjaRbnvC0c8pMbVxTFhFpw2s55MPTfR1niAIwlpitaTtSvfx5V9Rv13WZLfoOIxf2891+rEqeBbOmmC4vPhsHMdXJUlywwmOXThJsgx+/Q1L/PX1hy5FfefT/p63XnEdnq9Q2kMFTmpY2+UH7umyUa51j1DaRA1vdoXc2y5C7bmv49PUjlh1tVrxfIgq2Noo1IYJbrgODuzqvE/p9+T5Tm9pDZ5ruULpVo4fYEcmMGMbUbP7CO/4Gt7CVKfuablY3Vq8vLLgneQAACAASURBVEVr2+NQrQZkDXRjAW1ybFijWN9f+5N800Xkmy46/sn2Q5rn/hje/D5MdQxbGzn+awiCIJzhrKKC8RtwC9UORgHv7/ci/aTtfg/46SRJbgGI4/gKXD+YK/v9EOHUMTdb8Lr/Xudbt/e2Dgm9jD/4iU/z0sd8F2VKm4HSVNK5fDsvJpRCd7l/oxS6VsNe+lS48AkQVbE3Xo+689uo5W5FyxEopSCqwcAIZmwTduN2vMVJ1NQeJ6bSEFUULjrl+2138eU8ngVstUZ24dNQWmFGN2InthPc/S2UKdrjNNVBN/607nrN+SEKS3bps904shZ6YQoztA6CQyNv1ppD9p0UQYVi3Tmn9pqCIAhnEMHqqXl6fZIkzcO9Ecfxa/u9SD/i6a5l4QRQ2pnf0e8HCKeO3bsVP/czcPeOXuE0Gi3yFz/zB/zY1rtRVoGn0ctO3x1HAtRyJMj3nB8TOKPJ4XWwPYbILbtXW87De+D7qCzFmqIdoFLVAVRUxQ4OY57x3wALP/yG+wCtsWOb0UtTTgjhbDLxvLJ9ncV6AdllP47Z/rie8dtwwBWeVwaw1pBvexz+/D6YfMgZY/ohxWjXPQcRZngCb/5hKAq8+hSmMkQ+djaVHTeT3tMijEZJtz3xxFqsCIIgCMdFmq+a/2svKLumfCVJkmYcxz8OvBXXY/e9wEw/F+lHPN0Xx/Gzgf8st58G3AUQx/FHkyT59eMeunDc3Hef4uUvr7FrV29h+PaRh/nsz/w+F67f18ms+Z4zpoSOePA02g/KFXJu9Rzah7GN2Ge/HIbG3XHW4N39HVdjlJetVLDOyLJag8oAqrlIeMMXocgpxrdgxjajTEYxvAHv/pvb5pk2qqLCENK665sXVDBnxe5zlmapJN8CpWid7zycvOmd2KgKURWVNbDDE5C1KEY3Y9ad3blpU1C57wZ0fQ6VLmKDGnge3tw+dGseAh9/fi/5wn7MsBR3C4IgrDSrqBD6GuCHwFfiOB4D/hH4o/K9/43zejom/Yina8p/22uoAOI4/mS5T8TTCnPHHZqf/dkqk5O9wunyTffymZ/+KBtGllB+gDXGpeFKbybnveTO6RhedlJ51haouYfRX/0L8sdeiX3sMyFNUY05ZxSpM1fB5AVQdUaSGIPKl9AzS1g0tOqkP/4LUBlETe6EB28F7WODiOyKnyTYdQcsTKFMhhnb4tJs1lK77Svo5qIztmx8ldb5T8Hfczs0ZrALk9ggdNYCXoAZ6W1fqJem0Y15wKKMxS4bW5rOcg+rNNbvpPRU2nAr+KojEo0SBEE4xZhVUjAOTC93SInj+NXATUmSvKfc/st+L9KPePqDI0WX4jj+eL8fJJwYN92kedVVIXOLvcLpxRd9j//zkk9RiwqXjrOuuBsoa5MG0EXL2Q9o7UwqbVnD1FWMrbSGrIV3z03kFz0J/9Z/da1Hihwzsp5i22MI9v0IZTJXe9SYR7d9ngw6a7aNJf2HfwQDw9iwgg2r2PVbsZP3w8IktjqCGV5H8NAt5OvPc2aZy2PNWwT77kHlWelA3sD4nrNSiCrkmy/puXdTGcYGFVTewnq+S/n5EemWxxLtuQNrW+Tj211BO+DN7SV8+G6UKciHNpBu6U0bCoIgCCfHKioY725c+ELg74/w3lHpRzx99uAdcRz/9yRJrkuS5O39fpBw/PzHf3j8wi9UaTR6H8qrLvsmH33RXxBo0yWYOu/byiDqxa/F3nkDanKXq0HyAtTSHHiq7dmkSt8m7YFN64Rf/QtUfRa0wgY+Wiv07B5UVnfHNufRJusZi41qTjwZ4/rMFS1sEOLZjMrNX0K3lrCVGiqrE+6/39kaLBzAjG5GT+0AazCD65wg8vahjMEsu5cHVZQxLjVXHe18aBDRPPep+LO7MJURTG0YG1QJDtyLNikqCPDq02TWgNJ4C/tdnz2l8JamXERL9/PoC4IgCP0Qrp6C8Yk4jiOcm/hPAL/a9d6Wfi/Sz2+QP4zj+KeSJFkAiOP4ybhU3nXHMVjhOPnKV3ze8IYKadornN7w5H/hA8/9AlpZl0ZzhU2ABa3xwhCz9Vy8G/8BlWcU6zdBOICa3udcwrOG813y/Y7g0hqtgcZcaeWkwBbYdAE130LlGaa0EAA65pfaQ1WqqJm9+FM70WkDZQpUsYjyQ3RzEZU1sUFUptTKiFVriUb8XGqLk+i8hdecdlGmwXWut1zWxMua2CKjGJrAhoOHzI+tDZPVLu3Zp/JWZ2x5y32mp7FBte1xZf2Ka0AsCIIgnDJa+SM9gr75K+AhYAi4JkmS/XEcP6Hcf2O/F+lHPN2Lawb8ReAZwGuAPcc9XKFvrr/e5/Wvr1AUvcLpN571D7zzmf+E8jQqCCGqoVpL7Ua7eB54PnrfQ6jAWQV4k7spHnelM5+c3I3SIWRpl21T2XZF4dJ6XY16dVks7lqzaJTvap6MtWilsGHVfca+e1ClqeZynzpV5Fg8Z4TpBZjRLeh0CWUKioFxqnf+f2ibOc8pa/Gacy7dZw3K9zC4BsE2rLjice9QT6uDyUe24NVnsBjy4c2uDgrINlyI9XzX2mV0m9Q8CYIgnGLsKqkYT5Lk+jiOtwGVJEnmy30/AB5/PNfpRzy9F5gAvgnMAk8CFo9vuEK//Ou/erzhDYcKp6vfv8AbNt+D2uOjtIfWCps1YXDYCZ5GKaKKvGx/ogHnDO7/6PvovAlYrO9DNIpqlt/C5bYrqqtJcA+u+LzssetEiB9itI/S4KV19IEHySe2Ox+pInfNebUHgU929hPbPeZUY8G1YNl3F16R9YgYqz1U1sL6gWuholwzYS9rEO65ndZ5Tz/m3JmhCRoDz2L9aIWFua70olKuzkoQBEFYEczqqXkiSZIUSE/mGv2Ip38HBoA3AgnwYSACXnUyHywcyte/7vG611XJss5DqDB84mVf4JWXNtG7ZyEIOhJfK7Qt0EphKjVoLrl9UQTaw2oPWxnAay11rlfk2OH1GK3QaaOz+g7l9BaU4kW5qNHAGKo173rWgettNzBG+tgXUP3+PzgLgqKJXpwmP+sS9M4flAJOU4xuQlGg6jNQ5ES7fogyufOOUsqlz6zB+BUIq9i8CWEVY61L30UDbvVgfuxn3J/diTe3B7SHGbhcUnOCIAinkdXSnuVU0Y94mgOenSTJPoA4jt8EfHlFR7UG+eY3PV7zmmpPjZPC8L9f+hmuevx3YGorhBEs0Y7Y6DBAabBFDspDBT46CDrF4Aps1uBgBw5rCvLzLie697vlDteqRalSPfmuYFt7CoolF5nCK4WWh6cs4YM3o+k4eXuNOVrjW7DTztiSPMVrLUKRopdmsJVBtzIPC0VBUR1B5S3M4DqaF16JKjJo1Qkn78dqTTGwjnDqAbAF2djZHBVT4E/ej7LG9Z/bex+MnkArFkEQBOGEiPxVkrc7RfQjnt60LJwASkfON6/gmNYcN97oVtU1m73K/WM/9Tmuuvw7ZVpNObuBIEB5AQQeni37zymNURodVCh3uH+tE2AdFDYIUGEFrT1sVEWnzbIPnQbfb0e1FJSiibKWykNpjdUa3Vp0BdldWGuxtWHSc56Et3AAXZ9BZ84sU+UpRpXGnVkDZQtsbYx0c0y+0ZlmWs+HsEpraF37mo3xs50QK2uXjkQw/SAqb6KsBZN3ViAKgiAIp4Xm6nEYPyX0I552xnH8V0AVeC2ur91vreio1hC336545VUB9YPsCD7801/kF57yn+CF6EqEas5j1m3FTpyNOvAQXmsBl2ezrtDb9V9xJ3etonPr8JQTIdqD6hC6tYC3+3bwNUpXO8dbi8W0V6ZRmm2qZfHWvrQt04KlMaXnYWtjoDTFurMp1p2NnnuYaOcPoEjJx7aQbboY9eBNeHMNl47TCq8+x1EXaGgPV7d1dHRrARtUnAmm9vG3Xgxz2THPOy5M4dKRfigF54IgCAex1tJ2+tiH8GFcsXgrSZIl4Npyn3CS7NxheeXLfZYavZGV3/vJ6/jlp38L7ft4noeHRWPxZ/dih8ZRnnZRIV0KHO25aIt2ESLrh5jasLMRiCroKMRsuYDsif8PamDYNQy21kVqdOeBt9VhbDQAlQHwQ6wXYIMKJqyVtghdxypN6+zLsGMbsAPDFOvPbptlApiRjWQbL8BWh9HpItGO7+G1FlCBj7K5q52qHnsFXT+YcMC5mocDFMOb0WHllFy3TVrHm7oPb/pH6Lkdq2dZiSAIwmnC2JN7rTb6iTztTpLkz+M4vgIgSZJb4zieXeFxnfHMzsLPvQwenu79Rf++F32JNz3LNdtV2nOpNFxNEiYnuvtbTiAp5VbXKeVSeapsSRLW0LZA2axsqhthwxoqqKCxmOEJdGvRRVHcp5TXd07f2nd1VCaMaF74TGxthOj+78HSlEvVeQG2MkgxtB7PK53L/QCvMdeJWAHkKcHUA873qdl0Rp3tRsWKbGiCbOPFJzR3emEfOmtQVMew1VGy9RdgogGwlmJ48wld82io5hzYwkXhWouQNyConfLPEQRBWK1U1pjvcD+3u1yEYgHiOB4Azl+xEa0BWi34xV+scs+O3ul/07O+ztt//GuUTelQvu9SZsa4fcuRomVbAeVak+hlgeWHqMBD5QUYBVY5/yVyVLqE3ptgqkPY6jAqrVMMjEKRu9VsYQXyFFWkLitHQTD9IDZdT3b2YylGzyJ88Hv4cw+DUpjB9ei03jV6w7IIU415oj23OZGm3Bis0qXJpnK98roiWf7MQ+jGPKYyRD62/ahpMb24n2DmIVfQXp8m3fgYCCoUw2ed0u9RD17QEYbaBy889jmCIAhriEa2ttJ2/Yinf4vj+A4giuP4euAK4C0rO6wzF2PgLW+pcOONvVP/0sfdytUv+1cg6PSc8zzXwy1ruoO0ckXb5TnK810Kr6xBUlq5VWtYrKKsRRp20avlBsGNeVQQYn0PbXLydVvQs249QD6ykWBml2uR4gV4S9OQNfAnH6BpCtJzn0Ix9RB4IcXoWajmPGHeRBU5+ehZeIsHKAbWE8zuQudpOfaWsyJQPrZoorSHDaqYyrC7pcVJ/Nld7uvmPDaoUQz1NgImb6EbM9hwwDmkL9dfmdwZaAbHkaaztremq59Tautc2X3ecm1ipLWLIAhCD6sw83ZSHPO3QJIkfxfH8W3AC3BJl3ckSZKs+MjOUK65JuRLX+qtcXrauffzx6/+Wzydo3CO21YrzLot6LRVGk92Hk3X3Ddwjt8WVwyudLt/27JluBkch+oQxdAE/sxuwGBrw6jF6XaECTxaFzwVrKEY24rZcxfe7B4XZMmazsE8z6g+8B2KmR00z396WzzY6gitC56JWpom2ncHem4XJhokr405geIFmKBK45yn4C1OYvwaXuqKu4uhje5eirQr3Vf6O3VjCsLJxBloao98aLP7/CLFREPY6kj/k28K1NxO11DYr2BHzwbVR9mfUtiB9f1/jiAIwhpjFTUGPiX09Sd0kiT3APes8FjOeL7yf+ETn4h69l208WG+8Mt/yUCUo3wnqqy1KE+jsybZJc+E+hzRvd9BWbeyDa2xfuiiTL5fWg14kBeAE1IEAc0fezkEkXPYXpoFU2ArQ3jf/RsUYIIIXbRIx88GY4gevAlvaQoT1mhtuYxoxw/wm/PtNKG3NEUweT/Zhl4PJX/xALqsadKtBcz6C8isRWVN1yYlqFKUXk0563rOLYY34dVnUK0FV0s10luzpNJFVOZ61ilrUEVKa/PjUHkTG9T6Ez/LNEr7BKVQWZ2iMQu18f7PFwRBEA7LWltHI/mH08SP7lW85dd6a2U2DC3w97/6GcYHW13WAK4/nNIKigbq/u9iB8fQUYjNy6iMUm4VnB+isR0vJ7+0D1Dapb66Vp3ZsIo3uwvvwI+cSMutq5uyhvChm8FavKUpV0OVNfEX9tO86Eoqd/4rfrboBJTJsYXhYExlyFmpKrB+hKkMYQb6FCVKk268BG9+Ny7ylPes2rPhIDaIysiTxkTD5cq6Q5sFH5OD/aKO4R8lCIIg9EdFTDKFU83iIrz2NSELjY4o8HXB537lC5yzeZF825PwHrod1R34LL2VdFpHzTojS+UHWGvJN55PetEzqNzzbez8AZf6UpRF5gHWj9CB30mHFTmV+/4T3Zgrm+yGrvWKUiib4S9OgcnbK8rAutVrfkix4Ty8h5O2T5QNq2581qJai3hLk5hoiNamS9DNeVS6RLT7VkxllGziwr7qirzZB/HqMwCorEE+EXfe1B7p+hjdmMYGA9iyVgprUfUpyJtOSFVHj/2NiIYpBlJU1nT3EZ0aqwRBEIS1Tj07jizAGYCIpxXGWnj72ysk9/ZGOT708q/w9At2uNKgxSnyS68kSm5wZoxaddy9bXmRUoOYyjDp5S8BrWle9nz8ffdS3XMnprHkXMABVbTQC/vx9/wX+VmXohtz6MYsOm+5C9oWNhgEP0Q3F8s0YEQ+fBb4gYschYOEO7/vCr6jQZQxWG3x65Po1ry7ZtHEegGqKChq49hoEJ3VQSm8pQMUtXHM4LFrhZz4U52vD8aPMEMHpfOas+jFA25eWgsUXgTLwu6IH6RgYGLNFTYKgiCsNJK2E04pf/qnAV/+cq9wesVTbuVXnvMdAJTWqNYCXrYE1SqkLRflQbnl/X4I5KWhpYss6fmHMaObIayRb3s80ROeyuwPb8KffBBvaRpV5CjfJ9pzB/gh+fpzscu1QUqDF5CObyGY3+NW8JkcawPSLZe5GikgevC76LzhXMeVRSmDNhZaC3hZE+NF7nOWa52as9iiq2WLUtg+V6WZ6hgqraOsxVT6iCCBKyzvckZXRQvLMcSTIAiCsCKIeBJOGXf/F1z9gV7h9Jgt+/j4a//NWRFgwffQtkDvTZwWCCNMNEC+8XxnG9BaQNnlKJTFy5ao3PV1Gpc+n3D6IecCPvpU7OA4zO0uC8pL13EM4YF7yTdcQOvsy6nsvAW0h/EiovndruC8tDQw1dG2cHI/BWVtkylcw13tOcPLImv/lNjuFX7aA8+nGFiPyuqYygi21p8QMoMbMdGo+8ygPwFkq2PY5jzKZNig1knnCYIgCKcdWW0nnBKyDN7yq4pW1unNNlJr8rm3fZnoiU/DPnAzqrmA8srecdZisdjSQ8lsONeJoW7K/nW6SKnsvMU5jFtL8aNbCCYfRmduCT4mRSmN1R5Wu4a8Zt02GtEAXmMWf3Y3qr7UvqxVHqbmlvyr+izh5L2oInMZw6Dm2qkYi7UNMAYThKAVeXUdJhjAb82A8siHN5+4WWUQHfuYbrwAs+58V6ulfek3JwiC8AhS8Q9dTHR8rK6G7iKeVohPfCLktrt6BcHHfunfufC8HHbe6mqaKgMu/aR1OwVlwwGKs2KKsS3gR87Nul0H5CI8JhygfYJS2KyFbi2iixYoKMJBtEldnZLqCAs7uI58cJ0rzq5Ps9yapaiOkq07FwB/fo+rO9IeVoW0tj8FVZ/Bq0+B8vAWH27XY9naOMW6cymyJt7CPjAZ5Cl6aT86XcB6EcXYOcdnJ3A8KCUr5gRBEB4FSMG4cNLcdpvm4x/vtSV46VMSXvHsH7ngUdZwheCeTz68Hq8x71baaYWiAHIocoraGJ7WWOtEULo5dt5Pm2KCyQfwpx4A7eNtjUlnJrE2BxRKG9ABRntoZVHN+R4zydaWy8Bk6HSJfGgT2aZLXNoN3L/drUhQ2IF15APrwBTo1jwqa6BsgS1SsAZ/bhe6Ne9OTxfLeiTl7AVmHsRWRrHVMYkOCYIgnKGcjpqnOI6fD7wM2A/YJEk+cITjXgV8DhhKkmRxJcYi4ukU02zCr73RI887QmHDyBIf/5V/RxcZeKWFQBn1Ub4PQVAWiYPCED1wM+qB77ocsgowA2PkQxME9UnXFw5Dtvliso3OCmBwfIRiZBNqbi8qb+IauBiUMRSqemgvNj+ide7TDjv+bN15bmwmJx85q0fweAt7sCYHk2H9yBW5z+4E01ktZ4sC1V4amKMac6i0jm0tYsa2nZpJFgRBEB5VrLR4iuO4BlwLPCZJklYcx9fFcfy8JEm+dtBxlwCXruxoRDydcj796ZDkvt503R+94V/YOLiAUQpbGUQVmevx5nuu4NoPIGuBsa7tinVF2q6PXUHzgqdTfeA/3co2INx/L+mWx3WiRUB61mUUg+uJ9tyByhtup4V0dHvHm+lw5E10fQYbDWKjIfCCQxzEAciaePN7XMG41mAL1+a3SDHVcdTCXgDM4AawBtWaRxnbrkdSWf3QawqCIAhnBNVgxUNPTwMeSpJkeVn3DcBLgLZ4KgXWu4BfAX57JQcj4ukUsm+fOiRd9+rn3M5LrrgfAK002cgGsoue6Yq2G3N4zQWsH2KCCtm6cwnm9qAbc2VJU1fz2u7n8nASXymKkbPI6tMEk/ehUFhPEyzsppg4t0dotclTwv13O6sCpcjWXYhKF9GteaxfoRjd3vl8pTrpPGtdpCxrYqNhzNAmTK1su9KuQToLPb8XVZ92xfDhcTTvFQRBEFYVS+mK1zxtABa6tufLfd38HnB1kiRpHMesJCsqno6Vn4zjuAJ8FNgNXAhckyTJPXEcPwf4I+BAeegG4G+TJHl/HMfXAhd3XeYtSZLcvpL30S9XXx1Rr3fSXOODDT70mm87+4CicF5LXoAZ3UQ6ugnylGjHLajWEsXAOorxs/FbcxR+hG7NgYV8ZAuEVbIN5+NP78R6IdnEBUccgw2dM/iyvFJFyzlqRwOHHKta86VdgUJZi7f4MDpdABSkdaxfxZQNfPEjioEJ/KX9WGuxeNig6la7wWELt83QJpRfcVEq6SEnCIJwxnIaap72A91tIYbLfQDEcXw2MAb8bJdwekccx19JkuTmUz2YFRNPfeYn3wbsSJLkw3EcXwb8OfAsYA/w80mS3Fpe68+BvyzP2ZckyRtXatwnys03a/7u73oFxO++8ruMD2dgFdYPyEc2k579+Pb7qrWETpfQ6Rw6XSScvt/VC1mD8Z1jtmdaqLRBPn4O+fg5h3yuaszRvOtOwmYLUPj16Z73rQ6OmLaz0bBzCDe565AX1NCthS7zyd6lp8W68zGDG/DmdkOeuvSdd5RHSClsbezI7wuCIAhnBKdBPN0IbI/jOCpTd88APhXH8TiQJ0myE3jN8sFxHH8I+IPVWDB+zPxkuf3bAEmS3B7H8ePjOB5OkuSe5QPiON4IREmSPFTuGorj+D1ADiwB1yZJkq/gfRwTY+B3fqc3LfWYc2Z43QvvBr+cYu2jwggb1drHhNMPotMllLUom7nUXGkD4AQNqCJDN+YoDieAsibRw3dg8iZ+WQ/lTtZOgCmf1pYnHNkqwA9JN1zcqXkKBylMjkoXwIswgxsPOcVGQ+TrLkAvPozCUAwcHDUVBEEQ1hpmhcVTkiT1OI5/FfjDOI4PAD9MkuRrcRx/GJgGrgGI43gCV/ME8K44jj+dJMnuw1/1xFlJ8dRPfvJIx8x37XsTLoK1zOdxk5aXk/Zu4OqjDWRsrIbvr5wB13XXwS239O77gw9OE1YDt2wfUJ6PX60wNNGJOmbTVYoFH9Ks3ZAXcG1Yoip4Cl0boXrOOWj/0LRYMb1ECyea1HItkheAKrDhEN76rQxVDMF4FX3ECNEQMNHZ3PBYd+1Wncb+XVhrqYxvIhgcOei8R3dEaWJCmv52I/PRi8xHLzIfvch8HD8D4cqHnpIk+Srw1YP2veug7QPAB8vXirGS4umo+cl+jonjOAKuSJLkfcv7kiTplilfB36TY4inmZmVW+llLVx9dY1ud9QXvzjj8hesJ79r1BlSmgIDLI5dgD3gtKJqLRIs1vF0AJWIojZKNrKFYG4P+dB6zOBGdHMeMzAGM02gWX6gcxX3px9ANRfwjMJTisK6FJr1PExtHOtX8SZ3kwON/XvJNj32uO5Lze5E5W7eWo0mdvy8k5+s08TExBAHDiwc+8A1gsxHLzIfvch89HKmzMfpFoCLrbVlkrmSd9vOT5bbzwCuj+N4PI7j5UZk1+PSe5Q1T7clSdIddXol8NfdF43j+CNdmxcCP1qJwffLf/yHx2239Ua13v3uFJQmH5rAeiEmqkF1uMcjMjhwL166AH6IqY2QbnsSdmQT6bYnOj+kIMIMTaCyJmppCqxBL00R7rmNcOf38Ob2oPM61gvQmy4gW3cepjKIDWvu2MZs2c4FVLrE8WMP+6UgCIIgHIy1J/dabaxY5KnP/OQngY/Gcfw7wAXALx10mZcDP3PQvok4jq8B6kAMvGOl7qEfPvnJXmuCF70oI45dobUZ2YxZmkJhsTrAVDqpL9X9tNjD9wTSi/vxZ3agsBRLwyiTo2wBJnNO5AYsBm94HKaW260oFBbjBXi5KwWzh0n5HfLZyvXXI12EIsdWx6E+CdZgl20IVoiiyJ3g8wKXfhQEQRBWFStd8/RoY0WtCo6Vn0ySpAG8+Sjnv/gw+15zCod4Utx8s+aGG3qn8K1vTdtfF8ObSJVGNeYohjf1NL/NxrYRTt0H1pKPH955WzfnymiVQqcLmHCw7U5u0aA01vPxxzZRtCJU3kDlKaY6RjGwHmYeAGPJR4/g7N2cg/qU+7o67oRUY8Zt+xG2y+fJFDnYHOVFp1Tg5FmLtLWItRbPD4kqQyKgBEEQVhmrMXp0MohJ5knwx5/qnb5nPTPniU8sIzlFTjDzENiCfHSrS6d1YQbX0xxcf9Trm6CG15gFwAZV8rFzYH63S8MVKQpFMbjBiQ0/IF/fawqWT1xy9BtoznUiT8058MOOKWaR4fJ1CpPWMY0ZMAYVVtG1dadM4BSFW4yplKIoso4RpyAIgrBqGIwOn0Hpn5Vb1LUSiHg6QWZm4J//uTcd9rZf3ge41FwweR/e0gFnQNmqk259wtEvWJpVuma8DjN8FpkXoPIWxeBG8EPyded3jjcFBCfh3K26Hlatwa9C1nACJqi0LQ5sVm+Lk8qbbAAAIABJREFUGps3neBShz7oedYgTxsopQiiQfRhjDMPGYLysDZFKYXWWoSTIAjCKmShubYKxkU8nSBf/nJAlncelvO3LPKsKzvKWxWtthBQRQs9vxeUxgxMtL2cltHze/EW94NWFENbMANljZFyxpWqtYCeTCCoYYY2Q1hzlgR9iJOjMjhRpu2US9v5oWsibDKIhtuHKe1jlyNCyjusb5S1lry1BFishaxVJ6odbG9wKEFYa/tSef6pTQkKgiAIpwdJ2wl98bd/2ytcrnrxbhg4q72dD20kSOsoW2AVBHO7IG9hpx/ADKwrI0gKPb8bf2Evblmcj25MdcSTKfDmdrmmutZgTYFWGjN+bvkhTciaFPkJRp+8EIY29+47KL0IOCFV5O6nIxoibcxjMfhBDT+IDj3+OFBKER6tcbEgCILwqEcKxoVjcv/9iptv7k1bveJFe4GOeDLVEfLhjVg0XnMGlTdRGLA5ujmPXpoEBV59EmyBshaLgqj8lrRXvjUBW7ZMMVC0nJApUljYC9awuHsRok1Hb5VyFIwpKBqzTpz5FfzqcM/7WXMes1wblXac7rPWIp4fopRCKYUfDXSl7Q4jwgRBEIQzksFQap6EY3Dddb1Rp6c/7gDbzy5oAViLnt+DP7sTJ3p80NqFNC1Y7bnaIS9A5c740noRFBmmMkw+sg2yBmpuNyqrYyl9MLTfsROoHyhro1wqzaQpeE3wBk/ofkxrEZO3XNF2uoQOqm1Hc2st1uTtdJqxBnWEdi9+UMUPJIokCIKw1pCaJ+GYfP3rvdN21Qt3kg9thPoMwcz96LxZGktaLBajKs6mwI/Ar2Cqo9jqGLbI0ekS5E1nL1BaA6il/SiTluerHosDwBWKh8Og5sFalO9TtOahNYfyq6jq2HHWDnUdq2zvplIo7WHKNjOeX8HaAmsMQViVGiVBEARBap6Eo7O4CD/4Qa/CfsFzFjC18wkOJOjCiZ5lBaKwKAvWC8BaTG0cM1Q23PV88nUXdJ66xizYojxbuQJta50OUx5qOXVWGYVoANQmyFuoyMPOz2KwUGQoU+DVxtG6vzCoVxnC2hzKtN3Bq+TC6ihFVgflSVG3IAiCcAginoSj8p3veBRFRzxcdM4SExefjWotoA7uY6IUeXXcuYJbt239Xkfy5eNY3O+8lqCMTo1BaxFrysa/GGxQg8ENEA6448IBbFAjbex3wqnE5i1McxbdpzO4UoqgNn7U9/3lzxQEQRCEg5CCceGofPvbvVP2jKc2MIMTqMY02gtRJsdaKFQIYYVi/UWo5hyqtQBBDVsdO/yFTdrxODIZjGzFKg2Za85rLTCyFXVQUbjJ6i4iVS73B4XSGszJFu8JgiAIQn8MVYqTvMLqkiOra7SPAr797d5U2JVPnQcmsNVxcjR68QDkdVCuyFst7MEOb8UeJbIDQDAIWVkrFdackPIjSOuAxagAU7qNe9EgujTHVNov65J8bFGU7e00Ojqx4nFBEARBOF7mG1IwLhyBLIM77+x9QJ56ZcdjyVZHKaqjqLldqGwJTIFqLbjU27FsBKqjztXbFBC4Zf6qMuJW2RU5psiwxhVtF635tnjSfsTAwARz07PoMESFNZTSJ1SXZK0lzXOMMYS+j+etrqWjgiAIwiOD1DwJR2THDtVT77Rpk2Hd1qFDjrNBFdWYBQxWedCYdrVK3cdYS764H0yO8iO82jqUf6jZpVquNVqc7Jx70DG14VGWWicvdFpZRqPlLAvSomC4KqvpBEEQhGMjNU/CEbn/fs0T+T4At/AkzjvvCHVF1XFMfarsAeeDyQ85JF+acj3jUFBkWC9CVYYwRUbeWgQLfmUA7bkCcy8acnYEWHR0qGA7FRTGdPycjMFa27d4staSFRbfU2gRXIIgCGsKiTwJR+T++zW/wqexKN7Ip48snpSCygi0Fl0h9+FWqpm8bafk3KAcWXOhnZ7LmpZowNVK6SBCBxN9jzUrCrI8x9OaKOivB56nNS3retMFvndcwmlqyZDmFq1hvKYJ/bWV/xYEQVjLDFVOdpHS6vqdIeLpONiTLPFW/hqL4p18jHPPPYooGdgA0YgTT4exJ7BeiClaKGvROugq8O5+AI/+MDbTlCxLSYsWeWbxPY8wCCiMYanZ7HhEQV8CKjOazHqAxcfvWzylhSXN7bItFfXMEsqTJQiCsGaYk4Jx4UjE3/8iQ7jebq/kC5xzzquPfLBSrgD8MFhrMVisV3HtTsJaW6h44QBFa6n99ZGw1tLKWmCh3mhijEVrz6XatMaWKTgFFEUB/YinwqCUq53KDJgyDquVojCG+YbFAAOhohJ0flA8BVrRbiUTaEnbCYIgrCUkbScckRfu/LP212/gT7h/8OdP/GKlyFFobNdT5wdVvLJwvJ/Ij8VizLKjuaIwBdUgwPM8iqJAaU3QJZystSy0CnLjmu352iP0nBjytCIrXLTLWMXD8863Y7iqSXOoZ04TZoVlo9+ph/I9zVgNGrnF14paKOJJEARhLWHXWMW4iKcjEP3N5xn6rXei6vX2vu6Koyv4Ple8ohMZsrUaC9d8jNZVrzrmtZVSeEGFPK2jlMY7KELVj2hSSlEJItIsRfuKPDeAxfNcum2oWiUrCjyleiwHGpmhnhZYq8iNxdcFDQXgM1zx8bXzSV9qdX4Q6qnBU6rt4WltdwOacr4CTdRfaZUgCIJwhjFcPdmap9VljSPi6Qi0rnoV+eVPYvj1v4Cf3H3UY/OLL2H+T/+KIr647+sH0SB+UCM3Bc0shXyJSljBPw5vpSgMicKQ8fEaex+eRWtN0OUnlRYKYy01DL7n0mzLUa5laeTiT4qssFQCzUDkzm9kBaZwxeOeUgyEisxYjIFaKCvqBEEQhA6z9bVV87S27vY4KeKLmfmXf6f5ilce8ZjmVa9i5p+/0SOcrLUYa3rScYdDaU0zTSkKQ1EYGq3mcY/RWovWmigI28IpLQx75zNm6gULTcNMvcBai7WWaqCJfI0GPO1qorSCStArhsaqikqgqIaKkaoiCjQbBjWbhjUjVXlsBEEQhA7WntxrtSGRp2NRq7H0nvdR+eIXDvv2zG+8C79Wa2/nRUaj2QBr8f2ASrRyRpOtzDDfKphuzFIUUAk0Q5GinlpnMYUzLssLSys3zDUUhYFK6LFx2EWlsgICDZ7XK4iW65i6EcNMQRAE4XAYqXkSDsa/7QdHee9WOPvc9naWZW0ZneUZUVg5quiohCHNtNX++mDSwrDUKtAKBiMPTzuRs9QyzDZM29XVWEteGIxR+OVqt+VHOfAU9RTyMiXdSGEwtIS+xpMgkiAIgnCSrMbo0ckg4qkP/NtuBSALa7w+/RQKyx/xZgaoE91xB62ffFn7WKVU25l7+XU0Aj8g8A9faW2tZb5RUJQpN4CRqiYrDHNNJ5yWX6BIDfg5jAwpLB6t3OBrxUjVY77p6peUci9xExAEQRBOFaO1ky0YX12IeOoD/4c/IL/4Eu5+/2f57FVXAHATT+Hv1cs554d30uo6NgrdyjljLUEQnHCqy1qXassK59qtlMKUz6bpyRG7VXDGOqOl1DjBNlTxGOpavTBccWMqDFQD2gXkgiAIgnCyzCytrd8pIp76oLjkMcz/yWfYWK2xdath1y7NXVzKFfZ73Dr8Psa7jlVKUYmqR79emWvzjhL+mWtYllIwVqOtIfQgCjyMsQTaiaVlE8so9Mhyi4IjpuGUUozVJNwkCIIgnHqOtUDqTGNtScUTZOk974NaDaXgmc8s2vsb1Hi3/V/Hda3FVsHD8xn75jKmFjsNg621LLYMSy1TRp1cuxNPKwLfoxIETNcVu+dgrqmwaJTSaO1RCby2y/dQdMpuWxAEQRD6wpqTe602JPJ0nLzgBTl/8zedGqV//MeAX/7llCuuOPS738icGNIKhisa39MstQqKUqDXM8NAZqgEmum6pZG6/Wlh8TzIXX9gfAVLaVkArqCeQug5HydrYf1ISB46UScr4gRBEITTzejAKlRAJ4FEno6Tl7wk57LLip59731v5ZCVBtZa5psFuYG0gIW2Y3evuFleAZcVnWLutHA+SwORwqCYb3m0cjDGHZcaGKnCWBU2DML4UNBXcbogCIIgrATGnNxrtSGRp+NEa/jAB1q87GUdE6Sbb/b48pd9XvrSvPdg2/2l2xirKSYXLcY6C4FqGcQKPMhLTRZ64GlNXsBS6vStoiDwypV1VjFVV2wdWVs5ZkEQBOHRyczi2vrjXSJPJ8Azn1nwwhdmPfuuvjqiqw0eSikGIg+tLL6GwchNdej7bB4J2DwSsGHIb/s2jdcUozXcq+oewkZePowKDB66rHHSWrPG/MgEQRCERzHLXSxO9LXaEPF0grzvfS18v/MN37lT8+Y3V3rCj4ORZsNQwPpBn7BrGZxSyrVG6UqzKaUYjDSDkW7vD32LVi7RF3iWdTWLpyxaWUYqq+9hEwRBEM5Mun0HT+S12pC03Qly/vmW170u40/+pOMKfv31Af/zf1re//7WUc7sn/U1l+4zBoYjy2AEg5F7yqS8SRAEQXi0MHYaCsbjOH4+8DJgP2CTJPnAQe+/AvgZ4AfAk4HPJknyf1diLCKeToLf+q0W3/qWx113dcwoP/WpkHPOMbzmNdlRzuwPT8OmwV5JLqJJEARBeLQxvbCyv5ziOK4B1wKPSZKkFcfxdXEcPy9Jkq91HVYFfitJkh1xHF8O/C2w+sRTHyqxAnwU2A1cCFyTJMk95XsPAg+Wh+5OkuRV5f5zgN8FfgScA7wzSZLFlbyPIzE4CJ//fIMXvrDG/v2dtNy73x2xbZvhuc8tjnjuTF0x09BoBRuHinbhuCAIgiCsNk5D2dLTgIeSJFlO7dwAvARoi6ckST7TdfwFwH+t1GBWrOapSyW+PUmS9wOPi+P4eQcd9jZgR5IkHwI+Dvx513ufSZLkOeXrVV37rwU+XZ5zB/CbK3UP/bB1q+Xzn29Qq3WenKJQ/NIvVbn77sNPr7UwWddkRtEqFFN177DHCYIgCMJqwFh7Uq8+2AAsdG3Pl/t6iOO4Gsfx7wO/DrzzlNzcYVjJgvEjqcRuXgLcCJAkye3A4+M4Hi7fuzKO43fFcXx1HMdPB4jjOAB+HPjeUa552nn84w3XXttAqc4DsLSk+NjHwiOe0z3x/QQ7e/vZCYIgCMKjB2vsSb36YD8w1LU9XO7rIUmSRpIkvwm8CvhGqRtOOSuZtutHJR7pmHlc3vKmMoJ1SxzHPwksAY0kSexBxx+VsbEavr+y0Z1Xvxqmp+Ftb+vsUypgYuLw3zevWrBnxuArOHejRyU8so59YL9h55TFU3DxFsW6oUOPnZgY6tnOC8vsEgxXIQzWXqHUwfOx1pH56EXmoxeZj15kPo6f8cEV/4gbge1xHEdlUOYZwKfiOB4H8iRJ5uM4/nXgY6VG2AWsx9VBnXwR8kGspHjqRyUe8ZgkSW4q/63HcfwD3ER9AajGcazKyTms8jyYmZn6sQ45JbzylTAzE/CRj0Rs2GD5H/+jwYEDR16BsKnsH7ww16sgu7EW7t8XtS0Qkl2GC9f3PgcTE0McONC5QpbDnQ9HNDNN5Fsu2diiEqydsNXB87HWkfnoReajF5mPXs6U+TjdAnBqhaes1AK/CvxhHMcHgB8mSfK1OI4/DEwD1wAR8EdxHO8ALgHemiTJ/EqMZyXF0zFVInA9Lr33rTiOLwNuK9Xj84AgSZJ/Lq91AXBfkiRZHMffwC1BvKm85vUreA/HzZvfnPGmN2WndFWcry2pcX3sPHVsETRZ92hmumz1ophc8tg6mh/zPEEQBEE4EfqsWzopkiT5KvDVg/a9q+vr31vxQZSsmHjqUyV+EvhoHMe/gxNIv1Sevh94fxzHTwTOAq5LkuTb5XtvBN4bx/FPANuAd6zUPZwop1I4KQXbRjP2L/ooZdk6cmwRNBQZPG0xVqGwDERHXvUnCIIgCCfLanQJPxnUWrjhAwcWzuibPFyYebaumW14DFUK1q2xbtdnStj9VCHz0YvMRy8yH72cKfMxMTF0Wotdf//zJ/d79jdfdXrHe7KISeYZymjNMFpbW6JJEARBeGSYXJHKokcvIp4EQRAEQTgp1kASqwcRT8IxyQuwQCBenoIgCMJh6NOr6YxBxJNwVB444JHsc15V8aaMcyek+FwQBEHo5XSstns0IeJJOCo7pnwK4+r4HpryRTwJgiAIh7B+jfmKingSjsjOKc1Sy6XtfA8if239ZSEIgiD0x4G5tfX7QcSTcFgemtTctiPEWCeetowVXHpW+kgPSxAEQXgUYtfY4m4RT8JhmVly/fO0cg7n52/IqEWP8KAEQRCERyVrwTOymyN3oxXWNGeNFnjaYq3zjBqurq0fDEEQBKF/rDm512pDIk/CYdkwYrkyTpmrKzaNGjyR2YIgCMIRWD/6SI/g9CLiSTgiQ1XLkEScBEEQhGNwYGZt/a4Q8SQIgiAIwklhxCRTEE4N+2dh5yRsGYdN44/0aARBEISVYq0VjIt4ElaE6QX4tx9osgLu2gkvuNywcY3lxAVBENYKE2vs/3cRT8KKsHca0hyUgsK4bRFPgiAIZyb7pyXyJAgnzbYNcOcOS72lqISWbROQF5Yb/wvqLbhkG2zboB7pYQqCIAinAEnbCcIpYKgKL3myZdekZfM4DNfg23e4FJ5SsH8Ofu45Ft8TASUIgrDakcbAgnCKGKhAvLWz3UydcAJopZDlrmeeIAiCsLqxstpOEFaGx57jIk6NFly0FaqRRJ0EQRDOBDaMra3/z0U8CaeNTeOKq55tKQwE/tr6QRMEQTiTeXh6FfZYOQlEPAmnFa0VWlq9CIIgnFGISaYgCIIgCMJxIDVPgiAIgiAIx4FYFQiCIAiCIBwHG6VgXBAEQRAEoX/2TRWP9BBOKyKeBEEQBEE4KaRgXBAEQRAE4TiQmidBEARBEITjYNP42moXIeJJEARBEISTYu9k/kgP4bQi4kkQBEEQhJNCfJ4EQRAEQRCOA2ulPYsgCIIgCELfSORJEARBEAThONi0fm3JibV1t4IgCIIgnHL2Hsge6SGcVlZUPMVx/HzgZcB+wCZJ8oGD3q8AHwV2AxcC1yRJck8cx08G3gbcCsTATUmS/Gl5zrXAxV2XeUuSJLev5H0IgiAIgnBkTodJZh+a4jeBTcA+4EnAe5MkuXslxrJi4imO4xpwLfCYJElacRxfF8fx85Ik+VrXYW8DdiRJ8uE4ji8D/hx4FrAZ+GSSJDfFcRwA++M4/sckSSaBfUmSvHGlxi0IgiAIwvGx0gXjfWqKQeAdSZLYOI5fAXwE+KmVGM9KRp6eBjyUJEmr3L4BeAnQfaMvAX4bIEmS2+M4fnwcx8NJkvzTQdfKgeWY4FAcx+8p9y0B1yZJsrYMJgRBEAThUcRpKBg/pqZIkuR3u47XwOJKDWYlxdMGYKFre77c188x8137fg34X0mSzJXbnwd+mCRJHsfxh4F3A1cfbSBjYzV8/8x2P52YGHqkh/CoQuajF5mPXmQ+epH56EXm4/jZPLHiJdT9aAoA4jgOgV8E3rxSg1nJu90PdD+Bw+W+vo+J4/iVwECSJB9c3pckyS1dx38d+E2OIZ5mZurHNfDVxsTEEAcOLBz7wDXCic7HrbfP89VvTuL58LIXbeLcbbUVGN3pR56PXmQ+epH56OVMmY/TLQD37F/xgvF+NMWycPpj4D1Jkty3UoPRK3Vh4EZgexzHUbn9DOD6OI7H4zgeLvddjwvFUdY83ZYkyXy5/XpgQ5IkH4zj+LI4ji8q93+k6zMuBH60gvcgrCG+8vX97J9M2fv/t3fvwVZWZRzHvwcFRUBL5WJSiqP+0MHSvJJOySij1uS1UTMbQk3NEUEU8EIGoyAi4iUlL42YI2rjUDONYl4StcyiSJsseUhF84IJYd5IJDj9sdZpNgcOnH32fvc5e/P7zDDsvd93rf28D4f3PHu9a7/r7U94eP6yzg7HzKxuNK9truhPO2yyppDUE7gNmBkRCyWdVMjBUuDIU0SslPQ94CZJy0iX2n6VL7WtAKYBNwIzJE0EdgfOBJB0HHAd8Jyk44EdgFHAYqCvpGnAStI38cYWdQy2eWlqaip53ImBmJnVmaLnPLWzppgDDAEGSQLoBcwtIp6m5ubGvyvosmUfNPRBNsowc7V0NB8vLPqAR59aTvfu3Tjh6H4M/EzPAqKrPf98rMv5WJfzsa5GyUffvn1q+hHw3MtfrOj37K1T9qqrj6y+SaZZNmRwH4YM9kRRM7NyvfnPTzo7hJpy8WRmZmYV8dp2ZmZmZmVoXlvsTTK7GhdPZmZmVhGPPJmZmZmVYef+3Ts7hJpy8WRmZmYVeePtVZveqYG4eDIzM7OKrPVlOzMzM7P284RxMzMzszJsDjfcLuXiyczMzCoycECPzg6hplw8mZmZWUVef+vjzg6hplw8mZmZWUV8nyczMzOzMgwcsFVnh1BTTZvbJC8zMzOzSnTr7ADMzMzM6omLJzMzM7MyuHgyMzMzK4OLJzMzM7MyuHgyMzMzK4OLJzMzM7My+D5PXZykI4ETgXeA5oiYvIF9TgauBkZHxIP5tQOBMcBzgIAFEXFHzQIvQEdzUbKtHykfV0fEzTUIuVCV5EPSIcBwYC0wDBgZEa/XJPCCVJiPmcBq0gfKbYBREVHXK51uKh+SJgADgLeB/YErImJR3nY6sB+wBng5Im6rZexF6Gg+GvFcapXzyFMXJmkb4FbgwoiYBHxe0hGt9hkELANa/+LbCbgxImYA5wHTJe1YfNTFqDAXSOoGTAH+WHy0xaskH5K2BcZFxJURMQU4G1hRk8ALUmE+DgaOiIgJETEOOAwYWpPAC9KefAC9gbERcQ0wF7g2tx0IXAxcHBHjgbMk7VGz4AtQST5osHOpVYeLp65tKPBaRKzKz58Bvla6Q0QsiYj5rRtGxC8iYkHJS/8lfbKuVx3ORTYB+DHwbnEh1lQl+fgq8KGksZKuAL4YER8VG27hKsnHv4DekraUtCXQDCwpNNritScf34+IlrskdwM+zI+PAhaWbHsWOKbgeIvW4Xw04LnUqsDFU9fWD/ig5Pn7+bVynQ9MjYj3qhJV5+hwLiQNA1ZGxO+LCKyTVPKzsQtwMPBD4CpgVM5RPetwPiLiJeB24AHgp8DjpBGqetbufEjqAYwAJpbbto5Uko9SjXAutSpw8dS1vQP0KXm+bX6t3SSdBvSKiOurGVgnqCQXxwE9JV0C7AMMlzSyyvHVWiX5eB94LiJW53k9zwJfqXJ8tdbhfEg6FhgWESdExEnAIOC71Q+xptqVj1wo/Ai4PCJeLqdtnakkHy3bGuVcalXg4qlrexbYRVLLiouHAg9J2j7PW9koSWcB/SLiKkn7SNqzyGAL1uFcRMSYiJgWEdOAvwCPRcTsguMtWiU/G/OBXUue7wIsrn6INVVJPj5LmiTcYimwdQEx1tIm8yGpJ3AbMDMiFko6Ke/7CLC/pKb8fCjwcA1jL0Il+Wi0c6lVgRcG7uIkDQe+QbqMsDoiJkuaDqyIiGn5BHc5cCbwG+CeiHhE0nHA3aRviADsQPoG0ZM1P4gq6WguStqfQRp2fxOYFRF1/QuhknxIOo9UQK0GepImB9f7t8s6+n+lF+mX5mukb5cNAs6t93lg7cjHz4AhwFu5Sa+IODC3PR04gJSPxQ3ybbsO5aMRz6VWORdPZmZmZmXwZTszMzOzMrh4MjMzMyuDiyczMzOzMrh4MjMzMyuDiyczMzOzMrh4MrP1SJokaVIH2s2UVJWv8ErqJWmOpFfbse+urfeTdL+kozfUT8u2/PhwSU9WI2Yz2zy4eDKzqomIsVXs6yPSfZk6aizwRBv9jAWeqKBvM9uMbdnZAZjZ+iSdDAwnLVq7MzCOdCfsWcB2wDBgEiDgAuDbpILgUmA3YG/gsoh4WlI3YDLQi/SBaS0wLiLWSNoXuAx4FdgTeBRYSFo8mLx6/E/ya2318WVgKvAS8Hwbx7MXMId008VzgOX5+SsRMULSKcCxpBsUDiCtbr/e+nKS7iYt7rwG6AGMjog1ObbtJd0MLAJeAKYD83KeSvs4vGWbpJuA0cAeue1vgVOAQ4ALI+JeSXcCewGnRMQ/NnR8ZrZ58ciTWRcjScAPgHMi4hLgKWB6RPyBVGD0BnYkffj5ekQ8HxEX5eYLIuJsUkFwX16raySwU0SMjYgxpAVRR0jqDvwcmBIR44EzgEPzAsrzgHkRcX5+37b66AHcRypivkMqWtYTES8CE4DmiPhTLkKWAGflwuo64IyIGEe6+/ctbaTnoYgYnUe4mkh3jCbna0WO9+Z89+d5bcTy/20RsQK4Efh7bnsv8E3SufGp3OSl/G/hwsnMAI88mXVFw0lrq81KdRR9gK0AImKppIuAp0kjIa1Xd38m77dQ0nbAYOAYoL+kW/M+2wL987a+EfHn3GYF8K02YtpYH9tFxML8+q83clyPA3dIGgK8ByyNiNWSjgSej4hVJccwo40+eki6C/g3sD/rrklXFRGxUtIc4BxJk4G9I2Jqtd/HzOqXiyezrqeJtJ7YuS0vSOpdsj1IxcehwC830Vdz7u/BiLgm97UF6ZLX7nl7e2PaUB97trePiGiWNJu0tty7wF2t4ix9r/VIGgpcC+yWC5xJwBbtjL9cs4AnSSNpDxX0HmZWp3zZzqzreQw4QFIfAEn7Adfnx1sDo0iLto6QdFCrtkPzfgeQCqwAHiaNZrW4ADiRNDdouaQv5Db9Jd2e9/kY2ELSp/PCqBvr4/38fgCHbeLYZgOnAYPzpbyW492vZMX7L+X3a20HYCXwn/z8cyXbPiYXUpJGbiKG1tZrGxGLgb+S5kvNLbM/M2twXhjYrAuSdCpwKvAy8ClgPLA9aS7QCtIcpPlAX+CSiHgg3yJgDOlS2j6sO2H8KtKE8+XAKuDSPBK0LzAReI00j2lKRCzKBdstwBvAnaRNL1QRAAAA3ElEQVSJ5G310TJh/G+keUxTgZkl87BaH9sjwP0RMbvV8R4PLM3HdCGpUJoFnJD7nAHcQ5ow/wJwENCTVEwuIM1jeiu3m0uaFA5pMvnJJf38rmTb+Nz2UWAxsCQirswxnUa6ZDexrX8nM9s8uXgyaxCSmiNig5e8rP0k7RYRr0i6DrghIl7v7JjMrGvxZTuzBiDphvz3zM6OpQGMlnQv8J4LJzPbEI88mZmZmZXBI09mZmZmZXDxZGZmZlYGF09mZmZmZXDxZGZmZlYGF09mZmZmZXDxZGZmZlaG/wG/P0DR6gQMDgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.scatter(pvols, prets, c=prets / pvols,\n",
    "            marker='.', alpha=0.8, cmap='coolwarm')\n",
    "plt.plot(tvols, trets, 'b', lw=4.0)\n",
    "plt.plot(port_vol(opts['x']), port_ret(opts['x']),\n",
    "         'y*', markersize=15.0)\n",
    "plt.plot(port_vol(optv['x']), port_ret(optv['x']),\n",
    "         'r*', markersize=15.0)\n",
    "plt.xlabel('expected volatility')\n",
    "plt.ylabel('expected return')\n",
    "plt.colorbar(label='Sharpe ratio')\n",
    "# plt.savefig('../../images/ch13/stat_13.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Capital Market Line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "uuid": "b6eb023a-2407-49d7-986d-3d47e9c3ae45"
   },
   "outputs": [],
   "source": [
    "import scipy.interpolate as sci"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "uuid": "cca0eb49-0c77-4186-a2df-06ebf56fa923"
   },
   "outputs": [],
   "source": [
    "ind = np.argmin(tvols)  \n",
    "evols = tvols[ind:]  \n",
    "erets = trets[ind:]  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "uuid": "c3bf6d9e-0548-4874-90fc-0555f05afd5e"
   },
   "outputs": [],
   "source": [
    "tck = sci.splrep(evols, erets)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "uuid": "f37d6e01-0091-42d4-a9ca-1102f0fdb436"
   },
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    ''' Efficient frontier function (splines approximation). '''\n",
    "    return sci.splev(x, tck, der=0)\n",
    "def df(x):\n",
    "    ''' First derivative of efficient frontier function. '''\n",
    "    return sci.splev(x, tck, der=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "uuid": "e0a3d820-a9f1-41fa-a5bf-46fe176fdb68"
   },
   "outputs": [],
   "source": [
    "def equations(p, rf=0.01):\n",
    "    eq1 = rf - p[0]  \n",
    "    eq2 = rf + p[1] * p[2] - f(p[2])  \n",
    "    eq3 = p[1] - df(p[2])  \n",
    "    return eq1, eq2, eq3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "uuid": "2c23eced-0b5a-45cd-b677-f4eff5876f43"
   },
   "outputs": [],
   "source": [
    "opt = sco.fsolve(equations, [0.01, 0.5, 0.15])  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "uuid": "f4c2c1e9-aef7-4d22-9e1c-3b7ff5066830"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.01      , 0.84470952, 0.19525392])"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opt  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "uuid": "3651a6fa-7740-43fe-a18a-1134cbed7b0a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  0., -0.])"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.round(equations(opt), 6)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "uuid": "b4e45542-14a5-4e96-9bbe-186873d9f429"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7fd88190a150>"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.scatter(pvols, prets, c=(prets - 0.01) / pvols,\n",
    "            marker='.', cmap='coolwarm')\n",
    "plt.plot(evols, erets, 'b', lw=4.0)\n",
    "cx = np.linspace(0.0, 0.3)\n",
    "plt.plot(cx, opt[0] + opt[1] * cx, 'r', lw=1.5)\n",
    "plt.plot(opt[2], f(opt[2]), 'y*', markersize=15.0) \n",
    "plt.grid(True)\n",
    "plt.axhline(0, color='k', ls='--', lw=2.0)\n",
    "plt.axvline(0, color='k', ls='--', lw=2.0)\n",
    "plt.xlabel('expected volatility')\n",
    "plt.ylabel('expected return')\n",
    "plt.colorbar(label='Sharpe ratio')\n",
    "# plt.savefig('../../images/ch13/stat_14.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "uuid": "f2e04c2a-434a-442d-bce2-0f7be60c6e80"
   },
   "outputs": [],
   "source": [
    "cons = ({'type': 'eq', 'fun': lambda x:  port_ret(x) - f(opt[2])},\n",
    "        {'type': 'eq', 'fun': lambda x:  np.sum(x) - 1})  \n",
    "res = sco.minimize(port_vol, eweights, method='SLSQP',\n",
    "                   bounds=bnds, constraints=cons)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "uuid": "78362c70-0acf-4f13-9a7d-04adbc7de43a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.59 , 0.221, 0.189, 0.   ])"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res['x'].round(3)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1749328426359219"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "port_ret(res['x'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.19525371929484264"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "port_vol(res['x'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8959257896222954"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "port_ret(res['x']) / port_vol(res['x'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>\n",
    "\n",
    "<a href=\"http://tpq.io\" target=\"_blank\">http://tpq.io</a> | <a href=\"http://twitter.com/dyjh\" target=\"_blank\">@dyjh</a> | <a href=\"mailto:training@tpq.io\">training@tpq.io</a>"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
